A quadratic equation is of the form $ax^2 + bx + c = 0$, $a \neq 0$.

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3
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5answers
690 views

Quadratic formula not working?

Suppose I want to find the $ n $ for which $$(n)(n+1)/2 = 10 \Longrightarrow n^2 + n - 20 = 0$$ Clearly a solution is $4$. But, suppose we wanted to find that solution by use of quadratic formula. ...
-10
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0answers
26 views

If someone has a velocity of $32$ ft/sec, will they be able to ring the bell( more info below)? [closed]

At a carnival, a new attraction allows contestants to jump off a springboard onto a platform to be launched vertically into the air. The object is to ring a bell located $20$ ft overhead. The ...
0
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5answers
56 views

Why sometimes we get only one root of quadratic equations?

What is logic behind getting (sometimes) only one root of a quadratic equation which satisfies the equation?
4
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2answers
98 views

When the quadratic formula has square root of zero, how to proceed?

Is there an easier way to solve the following equation? $$x^2=2x-1$$ I think I know how to find $x$, using the quadratic formula: I get $$x^2-2x+1=0$$ then $$x=\frac{2 \pm \sqrt{4-4})}2= ...
1
vote
1answer
32 views

Quadratic Equations with the variable raised to a power higher than 2.

This is the problem in question - Solve the equation $ a^2 - 8a + 12 = 0 $. Hence find the four values of $x$ which satisfy the equation $ (x^2 - x)^2 - 8(x^2 - x) + 12 = 0 $. P.S. - I got the ...
1
vote
1answer
35 views

Symmetric Properties of Roots (Quadratic Roots)

What is the proof that - $α^2$ + $β^2$ = $(α+β)^2$ - 2αβ $α^3$ + $β^3$ = $(α+β)^3$ - 3αβ(α+β) $α^4+β^4$ = ($α^3+β^3$)(α+β) - αβ($α^2+β^2$) (α+β)4 = α4 + 6α3β + $4α^2β^2$ + $6αβ^3$ + $β^4$ ...
1
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2answers
22 views

Factoring Quadratic

I have used the substitution P = dy/dx to solve a first-order D.E of degree 4, so I got this: I have to show that the above statement can be written as: I tried to factor out first by taking p a ...
3
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3answers
32 views

How to rearrange a quadratic into its factorized form?

Like the title says, I'm a bit confused about how the smart people of past centuries figured out that the quadratic: $$ ax^2+bx+c = a(x-x_1)(x-x_2). $$ The book I have at hand shows how to do it the ...
4
votes
2answers
442 views

Solving an equation with exponentials

$$2^x+4^x+12=0$$ How exactly am I supposed to solve this? Am I supposed to get $x$ alone or solve it another way?
2
votes
1answer
35 views

Find cosine of acute angles in a right triangle.

If sides of a right triangle are in Geometric Progression, then find the cosines of acute angles of the triangle. [Answer] $\frac{\sqrt{5}-1}{2}$,$\sqrt\frac{\sqrt{5}-1}{2}$ My work: Using ...
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3answers
25 views

imaginary algebraic inequality equation

This problem was actually given to me as a typo. I decided to work it despite it being a typo and it presented a couple of questions regarding applying imaginary results to an inequality equation. ...
1
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2answers
32 views

Find the value of $2p+4q+7r$ given that $2p,\ q,\ 2r$ are in geometric progression.

It is given that $2p,\ q, \ 2r$ are in G.P. Also the roots of the quadratic equation $$px^2+qx+r=0$$ are of the form $\alpha ^2,\ 4\alpha -4$. Find the value of $2p+4q+7r$. From the given data: ...
0
votes
0answers
70 views

How can I check these equations if they have a solution?

I have two equations which are: $p^3+k\equiv0 (mod \quad h) $ and $(3p^2+3mp+m^2)m\equiv 0(mod \quad h)$ where $k,h,m >0$ and $p\ge0$ and $h\nmid m$ I need to show for given k,m,h and for all ...
1
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5answers
23 views

How to find the equation for a parabola for which you are given two points and the vertex?

I was originally given the value $(4,-2)$ as the vertex of a parabola and told that it also includes the value $(3,-5)$. From this point, I deduced that the next point would have the same y-value as ...
0
votes
1answer
35 views

How to solve the equation $y = \frac{x^2}{20000} + 0.0046x + 62.054$ for $x$?

So I have an equation I am trying to solve for x. $y = \frac{x^2}{20000} + 0.0046x + 62.054$ I can solve it up until this part, and then my mind just blanks. $$\left(\frac{y-62.054}{0.0046}\right) ...
1
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3answers
54 views

Is there any methods to solve for integer solution of a quadratic equation like $ax^2 + bx + c = 0$

Is there any method to solve for integer solution of a quadratic equation like following: $$ax^2 + bx + c = 0$$ where $a, b, c \in \mathbb{Z}$ If not is it possible for the Special case: ? $$x^2 -x ...
1
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1answer
34 views

Law of Indices and Quadratic Expressions

So I think I need some clarification about the rules for manipulating indices, in particular these two equivalences: $(x^3)^2 = x^{(3)(2)} = x^6$ $a = a^1$ Take the expression: $(5+5)^2$, which is ...
0
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2answers
35 views

If $ax^2+bx+6=0$ doesn't have $2$ distinct real roots, then find the least value of $ (3a+b)$

If $ax^2+bx+6=0$ doesn't have $2$ distinct real roots, then find the least value of $(3a+b)$ $a,b\in \mathbb R$ Any hint for this question?
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2answers
28 views

Quadratic Equations GRE Quants

It would be very useful if someone can give me an answer to this question with a proper explanation. One of the factors of the equation $x^2 +9x + c$ is $(x+11)$, where $c$ is a constant. Which of ...
0
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2answers
26 views

quadratic equation max and min problem

A transit company charges $1.25$ dollars per ride and currently averages $10,000$ riders per day. The company needs to increase revenue but found that for each $0.10$ dollars increase in fare the ...
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1answer
19 views

max and minimum qudratic function problem

A piece of wire $20$ metres long is cut into $2$ pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum. ...
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5answers
50 views

solve this equation for $x$ : $y=x-6\sqrt{x}$

solve for $x$ this equation : $$y=x-6\sqrt{x}$$ I've tried raising everything to the power of two but it doesn't work $x$ shouldn't have two values.
0
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1answer
14 views

Finding the y-vertex of a function and X2.

I am trying to solve the following exercise: The graph of the fuction $y=-2x^2+bx+c$ passes through the point (1,0) and has as its vertex the point (3,S). What is the value of s? Options: A -5_____ ...
-1
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1answer
29 views

Determine how real parameters a,b,c are ordered [closed]

We are told that the real-valued function $f(x) = \frac{(x-a)(x-b)}{(x-c)}$, defined except where $x=c$, will assume all real values. Can we say what is the relationship between a, b, c? E.g. is $a ...
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0answers
16 views

Probabilty of even number of games won/lost uses auxiliary variables for a quadratic equation. Why?

In a problem of finding the probability that an even number of games (even S) not being lost in $l$ games, I read the following explanation : "We form the equation, $x^2 - 4rx + 2r^2 = 0$, and ...
2
votes
3answers
49 views

Quadratic Equations - One rational solution?

I have a question that I am working on: Which of the following will give one rational solution? 4x^2 = 9 4x^2 - 12x = -9 x^2 = 5 x^2 - 2x + 14 = 0 2x^2 = x I am ...
0
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1answer
26 views

Factorizing Given Problem

I have searched through various site's and forums but couldn't find the answer to my problem, $$z^2-\frac{1}{2}z-\frac{1}{4}=0$$ How will you factorize this As I can't find $2$ numbers that give me ...
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2answers
33 views

Finding out the quadratic equation using Vieta? [closed]

So I have the solutions to a quadratic equation: $x_1=\frac{-3}{2}$ $x_2=\frac{1}{4}$ $x^2+px+q=0$ (Just telling you as I've seen many people using other letters for the variables) I tried ...
0
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1answer
21 views

What can the “Product of Roots” be used for in quadratic form?

If I have a linear function and some kind of quadratic in x and y ie: $x^2+xy+y^2=1$ that share two roots, then I can substitute that linear function into the quadratic expression and use the Sum of ...
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0answers
17 views

Linear constraints in Quadratic equation

I have been going through this paper, and wish to implement the same algorithm in java. I have also managed to write equivalent code for the same, but I have not completely understood the mathematics ...
0
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1answer
18 views

Grade 10 Quadratic equation

This was on my year 10 maths test and I gave up with 40 mins to complete: Basically you were given the coordinates: y intercept : (0,10) 1 x intercept: (10,0) and y value of the vertex: +15 Can ...
34
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4answers
2k views

Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?

I understand that the quadratic equation can solve any second order polynomial. Furthermore, equations exist for polynomials up to fourth order. However, without a graduate level degree and a deep ...
0
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1answer
30 views

Solve quadratic equations modulo prime powers

To find if $x^2 = a \mod p$, I use the Tonelli-Shanks algorithm. However, how do I find the roots for $x^2 = a \mod p^t$, if I have solved the previous equation? Thanks
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2answers
35 views

Solving Complex Quadratic equations

After working a few exercises on the topic, the questions become progressively harder. In this particular exercise I was asked to solve the equations. However I can't quite seem to break this problem ...
0
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3answers
48 views

Where am I going wrong with this completing the square exercise?

I have been trying to learn some pre-calculus stuff in advance for next year (attempting a university paper) I am trying to solve a completing the square equation but can't see where I am going wrong ...
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3answers
36 views

solve quadratic equation

I'm trying to solve the following equation $2t^2 + t - 3 = 0$ I start by dividing by 2, $t^2 + \frac {t}{2} - \frac {3}{2} = 0$ Then I solve for t $t = - \frac{ \frac {1}{2} }{2} \binom{+}{-} ...
0
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2answers
19 views

Finding the other $x$-intecept of a quadratic equation $ax^2+bx+c=0$ when $a$ is unknown and one $x$-intercept is known

One of the $x$-intercepts of the function $f(x)=ax^2-3x+1$ is at $x=-1$. Determine $a$ and the other $x$-intercept. I happen to know that $a=-4$ and the other $x$-intercept is at $x=\frac{1}{4}$ but ...
3
votes
1answer
95 views

Quadratic equation, math olympiad question

So this is a 9-10th grade, math olympiad problem I found. Define the parabola $y=ax^2+bx+c$ such that $a,b,c$ are positive integers. Suppose that the roots of the quadratic equation $ax^2+bx+c=0$ are ...
-1
votes
3answers
23 views

Conditions on polynomials with common roots.

If one root of the equation $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ is common and $a \ne b$ then: The options are as follows: $$\begin{array}{ll} (A)\quad& a + b = 0\\ (B)& a + b = -1\\ ...
1
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4answers
32 views

How do you find out the range of values when dealing with simultaneous equations?

Find the range of value for $k$ for which $kx + y = 3$ meets $x^2 + y^2 = 5$ in two distinct points. im so stuck can someone give me a clear guide to the correct method and answer, thank you
0
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1answer
38 views

Parametrization of $ax^2+bxy+c=0$

Can I just fix $y=t$ and use quadratic formula to get the rational points of the diophantine $$ax^2+bxy+c=0?$$ or is there another method? I feel like I am turning in circles with the quadratic ...
0
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3answers
45 views

quadratics equation tricky problem

I am confused with this question- if $ax^2+bx+c$ have no real roots then- $1+c/a+b/a$ is-- a. Positive b. Negative c. Zero d. Can.t say I tried attempting it as follows $b^2-4ac<0$ so ...
0
votes
1answer
37 views

Question about quadratic equation of complex coefficients.

Let $az^2+bz+c=0$ be a quadratic equation with complex coefficients $a,b,c$ and roots $z_1, z_2.$ If it is given that $|z_1|\not=|z_2|,$ how can I obtain the condition for this containing $a,b,c?$ ...
0
votes
1answer
37 views

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$ My Procedure The roots are $$\frac{-b+\sqrt{b^{2}-4ac}}{2a}$$ and ...
1
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1answer
53 views

Non-standard quadratic matrix equation

I have an equation that looks like the following: $$ A\cdot\mathrm{diag}(x)\cdot x + B\cdot x + c = 0 $$ where $A, B, C \in \mathbb{R}^{n \times n}$ and $x, c \in \mathbb{R}^n$. $ x $ is unknown. ...
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1answer
40 views

List the elements of the set $\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$ [closed]

I don't get this maths equation Can anybody explain it ? Thanks List the elements of the following set: $A=\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$.
0
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0answers
18 views

About diagonalizing a matrix for a quadratic expression (with the goal of uncoupling mixed terms)

my question is originated from a physical problem. I will try to present the problem as simple as possible, but I fear it will still be long since I'm bad at expressing myself briefly. It starts with ...
0
votes
1answer
46 views

Solve system with different variables

I need to solve the system: $$x^2+2xy+y^2-1 = 0$$ where variable is $x$ AND $$x^2 + 2xy = 0$$ where variable is $y$. From the first Ι take discriminant, and end in one solution $x_1 = 1-y$ and ...
0
votes
1answer
37 views

In what base does the equation $x^2 - 11x + 22 = 0$ have solutions $6$ and $3$?

If we have below equation and know that $6$ and $3$ are answers of this equation, how to obtain the base used in the equation? $$x^2 - 11x + 22 = 0$$ Partial result The base is not $10$. (Because ...
2
votes
3answers
37 views

Manipulate the Physics Equation $P = I^2R$ to get R by itself

Given that $P = (V^2 R_1)/(R_1 + R_2)^2$, manipulate the equation so that we get $R_1$ by itself and that we have a quadratic equation. Where $V, P, R_1$, and $R_2$, are variables. I'm stuck when I ...