Questions on quadratic equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-h)^2+k$ or $y=a(bx+c)(cx+d)$.

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2answers
42 views

Find the value of $f(x)$ for $x = 2 + 2^{2/3} + 2^{1/3}$

If $x = 2 + 2^{2/3} + 2^{1/3}$, then find the value of $f(x)=x^3 - 6x^2 + 6x$. I am unable to get to the answer - end up with more than one term. Please help me solve this!
-1
votes
1answer
69 views

Quadratics Challenge [on hold]

my teacher gave me this as homework. Im in the advanced math class for grade 10 and this is the A grade question. If anyone can do this with the working out and an explanation that'd be great. ...
1
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1answer
30 views

For the given quadratic equation find the value of p

For the equation 3x^2 + px + 3 = 0 , p>0, if one of the roots is square of the other, then p is equal to? Solving the equation, i get the value of p as -6 but the question states that p>0. Is there ...
0
votes
2answers
14 views

Quadratic Function: X intercepts.

A quadratic function with a y-intercept of 0 and an axis of symmetry of x=-1. Apparently, there is suppose to be 2 x-intercepts, which I really don't understand. How can the parabola cross the x ...
0
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2answers
18 views

Quadratic Functions word problem.

I have the quadratic function $$y=\frac{1}{294}(x-84)^2-24$$ that represents the shape of the cables of a certain bridge. I am suppose to be determining the vertical height of the cables above the ...
2
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1answer
18 views

What is the spherical parametrization of an ellipsoid NOT centered in the origin?

I would like to know how to parametrize an ellipsoid not centered in the origin, but with its axes parallel to the main axes of the reference system. The result I am looking for would be an ...
0
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2answers
28 views

Quadratic Functions Problem

Question: The main section of a certain bridge has cables in the shape of a parabola. Suppose that the points on the tops of the towers where the cables are attached are 168m apart and 24 vertically ...
1
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5answers
51 views

For what real number $c$, this equation has exactly three solutions?

For what real number c does the equation $|x^2 + 12x + 34| = c$ has exactly three solutions?
-2
votes
0answers
38 views

Using quadratic equations for problem solving [on hold]

The numerator of a fraction is 3 less than the denominator. If the numerator is increased by 6 and the denominator is increased by 5, the fraction is doubled in value. Find the original fraction. At ...
0
votes
3answers
18 views

Finding dimensions using quadratic formula

A 52 m long fence is constructed on three sides of a housing block with area 240 m^2. The fourth side facing the road is left open. Find the dimensions of the block. Also here's another question I ...
-1
votes
1answer
22 views

Rearranging to quadratic equation [on hold]

How do I rearrange this to a quadratic equation? $$(3x-7)^2 = x^2 + (2x-1)^2 $$
1
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1answer
29 views

Quadratics: Solve for B and C.

If I know that the points (-1,6) and (2,3) are on the graph of the quadratic function f(x) = 2x^2 + bx + c, how do I determine b and c? Thanks to anyone who helps.
0
votes
1answer
19 views

Quadratic Functions: Determine the value of b

I'm having trouble with this question and I'm not sure what to do. Would appreciate any one who helps me out. Question: The point $(-2,1)$ is on the graph of the quadratic function: $f(x) = -x^2 + bx ...
1
vote
2answers
44 views

Quadratic Formula for complex variable with real coefficients

I have been upto proving the following $$(\forall x\in \mathbb C, ax^2 + b x + c = 0) \land(a\neq0)\Leftrightarrow (x = {\frac {-b \pm \sqrt{b^{2}-4ac}} {2a}})$$ Due to equality we need to proof bi ...
0
votes
0answers
16 views

Need to solve two equations simultaneously to get a quadratic.

$(1)$ $p=c=4-\frac{2x}{p}$ $(2)$ $c=p=\frac{2x}{c}-4$ I want to plug $1$ into $2$ and $2$ into $1$ I need to get two answers to put into quadratic form. Could you also help me with the working ...
0
votes
2answers
36 views

Consider a quadratic equation

$x^2-2(a+1)x+3a+2=0$ Where a is any real number. Find all values of a so that the equation has two distinct real roots. I tried solving for a by using the inequality $b^2-4ac\gt0$... but when i ...
10
votes
6answers
1k views

what would be the way to solve a system of equations like this one?

Solve: $xy=-30$ $x+y=13$ {15, -2} is a particular solution, but, how would I know if is the only solution, or what would be the way to solve this without "guessing" ?
0
votes
1answer
18 views

Quadratic problem

NASA launches a rocket at $t = 0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t) = -4.9t^2 + 37 t + 101$. Assuming that the rocket will splash down into the ...
0
votes
2answers
43 views

Equation with the discriminant

I'm stuck on my maths homework, and would appreciate help. The question is: Show that if the equation $(m + n)x^2 - 2mnx - (m-n) = 0$ has equal roots, then $$m^2 = \frac{n^2}{1-n^2}$$ I've worked ...
1
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1answer
39 views

What is the relationship between three points on a quadratic curve and the curves coefficients?

In other words, is there a formula to get the coefficients a,b and c in terms of three points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3, y_3)$? I am asking this because I have a linear algebra problem that ...
0
votes
0answers
9 views

Question on simple quadratic word problem regarding weekly revenue when price of merchandise is lowered

A store owner sells headphones at 24 dollars a piece with roughly 1000 sold per week. The store owner finds that for every 1 dollar decrease on the price per headphone he sells 100 more headphones per ...
0
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2answers
39 views

Can one solve this system of qudratic equations unambigiously?

Given the parameters $p_1, p_2, p_3$ I want to know if the following system can be solved: $p_1 a + p_2 c + ef = 0\\ p_1 b + cd + p_3 f = 0\\ ab + p_2 d + p_3 f = 0\\ p_1^2 +a^2+b^2=1\\ ...
2
votes
2answers
73 views

If the equation $|x^2+bx+c|=k$ has four real roots …

If the equation $|x^2+bx+c|=k$ has four real roots then which of the following option is correct : (a) $b^2-4c >0$ and $0<k<\frac{4c-b^2}{4}$ (b) $b^2-4c <0$ and ...
0
votes
3answers
31 views

Tangent of a rational function

I'm wondering if someone could help me solve a little conundrum I've been having. I'm trying to find the equation of a line with slope $-1$ tangent to the curve of a rational function. The function is ...
13
votes
10answers
4k views

Taking Calculus in a few days and I still don't know how to factorize quadratics

Taking Calculus in a few days and I still don't know how to factorize quadratics with a coefficient in front of the 'x' term. I just don't understand any explanation. My teacher gave up and said just ...
2
votes
2answers
66 views

Quadratic Prime

We had received some questions on Quadratic equations, But I wasnt able to do one. Here it goes: Let $a,b$ be natural numbers $a>1$. Also, $p$ is a prime number. If $ax^2+bx+c=p$ for 2 distinct ...
1
vote
2answers
22 views

How to Find The Roots of this Quadratic Given Sum & Product

My question is: The sum of the roots of a quadratic is $55/72$, and the products of the roots is $-25/12$. Find the roots. How I'm trying to do it so far: (Also, please correct my thought process if ...
0
votes
1answer
39 views

Solve the equation $x^2+bx+c+t\log(x)=0$

There is a explicit formula to solve the equation $x^2+bx+c+t\log(x)=0$ with the constraint $x>0$?
2
votes
5answers
72 views

Algebraic process to find numbers so that $xy=45$ and $x+y=18$

Can someone help me with the following question? The sum of two numbers is $18$ and their product is $45$. Find the numbers. I know that the answer is $15$ and $3$. But how do I find that answer ...
1
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1answer
40 views

Quadratic equations - finding value of x

Question: Solve the equation $$\frac{2x}{3x^2 - x+2} - \frac{7x}{3x^2 + 5x+2} = 1$$ I attempted to split the two quadratic equations into their roots, however, was unable to do so. Then I tried to ...
2
votes
4answers
55 views

Quadratic equation - solving for x

Question: Solve the equation $$(x+2)(x+3)(x+8)(x+12) = 4x^2$$ I tried to solve the equation by expanding the LHS and then equating it to the RHS, but that just doesn't seem to be feasible. I am ...
1
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7answers
231 views

How to solve the quadratic equation $x^2-1=2$?

Solve $x^2-1=2$ I have no idea how to do this can somebody please help me? I have tried working it out and I could never get the answer.
2
votes
3answers
70 views

How do I factor this quadratic?

I'm going through the AoPS Algebra book, and I'm on the quadratics section. I'm given this challenge question: $ \displaystyle 2x^2 + 7x(\sqrt{3}) + 9 = 0$ And I have to solve for ...
2
votes
2answers
58 views

Using factoring to solve the equation $(r^2 + 5r - 24)(r^2 - 3r + 2) = (4r - 10)(r^2 + 5r - 24)$

Solve for all values of $r$: $$(r^2 + 5r - 24)(r^2 - 3r + 2) = (4r - 10)(r^2 + 5r - 24)$$ I'm not sure how my thinking isn't really correct here. I know this all seems very elementary and such, ...
1
vote
1answer
39 views

Quadratic equations ..

The set of non-zero values of k such that the equation $|x^2-10x+9| =kx$ is satisfied by atleast one and atmost three values of x, lies in _. The answer is $(-\infty, -16] \cup [4 , \infty) $. How ...
2
votes
4answers
65 views

Show that $ax^2+2hxy+by^2$ is positive definite when $h^2<ab$

The question asks to "show that the condition for $P(x,y)=ax^2+2hxy+by^2$ ($a$,$b$ and $h$ not all zero) to be positive definite is that $h^2<ab$, and that $P(x,y)$ has the same sign as $a$." Now ...
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votes
2answers
77 views

How to write these quadratic equation in general form? [closed]

Write the quadratic equation in general form: 1. $x^2=16x$ 2. $13-3(x+7)^2=0$ 3. $x(x+2)=5x^2+1$
2
votes
2answers
31 views

Quadratic equation not equal to zero (solving a matrix with a parameter)

I came across this in my matrix module, learning about number of solutions when the matrix has parameters. $$ \left[ \begin{array}{ccc|c} 1 & ...
0
votes
3answers
58 views

How to solve this word problem on the topic of quadratic equations?

The maths teacher of Mumbai is transferred to another school. The students of Class 10 decided to buy a book for 360 rupees(currency) as a gift for her. On the farewell day, 4 students did not turn up ...
0
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1answer
40 views

Difference between Half Quadratic vs Quadratic

Half quadratic minimization/penalty/optimization, I am unable to find any related material/resources. If anyone can point to some useful resources, it will be great
0
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1answer
19 views

Check if a point is within a quadratic surface (with arbitrary rotation)

Is there a general way to check whether a point is on a quadratic surface given that the principal axes do not need to coincide with the coordinate axes and that the quadric's centroid does not need ...
0
votes
4answers
48 views

One root of the equation $x^2-(r+3)x+(5r-3)=0$ is twice the other root. Find the two possible values of r. [closed]

One root of the equation $x^2-(r+3)x+(5r-3)=0$ is twice the other root. Find the two possible values of $r$. I need help with this question, thank you.
1
vote
2answers
40 views

Can I perform the quadratic formula on polynomial with complex coefficient?

2 weeks ago, we had a Math test on complex number. One of the question was: Let $z=x+iy$ be a non-zero complex number, where $x,y \in \mathbb{R}$. Given that $z+\frac{1}{z} = k$, where $k$ ...
0
votes
1answer
36 views

Cross section of parabolic satellite in Quadratic Functions

A parabolic satellite dish has a cross section that can be modelled by the equation $$y = 0.05\,x^2.$$ While still in the shipping yard, the dish fills with rain. The rain forms a circular puddle with ...
0
votes
3answers
75 views

Absolute value quadratic inequalities not the usual?

$ | -x^2 + 6x | \gt 13 $,for example. I would start off solving $ -x^2 + 6x = \pm 13 $ and either get 4 solutions, 3 solutions or two simply do the the nature of the graph. Without knowing if the two ...
3
votes
5answers
795 views

Where did $-4x$ come from?

I'm going over my quadratic equations for the ACT and I came across this quadratic: $$(x – 2)^2 – 12$$ My teacher said we could have factored it out into this: $$x^2 – 4x – 8$$ But I just don't ...
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votes
3answers
71 views

Finding parametric distance on quadratic curve from given $(x,y)$ point

I want to get the parametric distance (the "$t$" value) at a location on a quadratic Bezier curve, given the "$x$" and "$y$" coordinates of the point. I have start point, end point and control point ...
0
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3answers
40 views

where am I going wrong with solving this equation?

solve $z^2=2e^{5{\pi}i/6}$. Well, clearly $z={\sqrt{2}}e^{5{\pi}i/12}$ is a root so its' conjugate $z={\sqrt{2}}e^{-5{\pi}i/12}$ is the other root. But I can also argue ...
4
votes
2answers
191 views

Solving awkward quadratic equation to obtain “nice” solution.

I would like to solve the following quadratic equation to get a "nice" analytic solution for $\rho$. $\rho^2(r\sin\theta-2nr^2)+\rho(2nr^3-2r^2\sin\theta-2\sin\theta+2nr)-2nr^2+3r\sin\theta=0$ where ...
3
votes
2answers
72 views

Solution for this Logarithmic Equation

Recently I was going through a problem from the book Problems in Mathematics - *V Govorov & P Dybov* . $$(x-2)^{\log^2(x-2)+\log(x-2)^5-12}=10^2\log(x-2)$$ I tried solving by first considering ...