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

learn more… | top users | synonyms

1
vote
1answer
40 views

Quadratic inequality with parameter

Hi I've got this inequality with parameter $a\in R$ $\frac{x+a}{x}\le x+2$ I've solved it but I've got different results than book. I've done it by dividing it into 2 cases. 1. x<0 2. x>0 and then ...
0
votes
1answer
34 views

Modulo Quadratic Polynomials

Can you, given a large number N, find a, b, c such that ax^2 + bx + c = 0 has at least N roots? All of this is in any mod you choose.
1
vote
1answer
38 views

Quadratics Word Problem

The path of a football flying through the air can be modelled by a quadratic equation. The football reaches the ground after 12 seconds in flight and is kicked from a height of 1 meter. The parabola ...
1
vote
3answers
34 views

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions?

Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions? Equation: $$0 = 3x^2 + tx + 10$$ Can you please explain the answer in simple terms, ...
1
vote
2answers
55 views

Solve $f(x) = ax^2 + bx + c$ to find the value of $K$

$f(x)=ax^2+bx+c$, where $a=-9$, $b=12$ and $c=16$. If $$-1<f'(x)<1$$ then $h<x<k$. To $2$ decimal places, what is the value of $k$? Hi, this is working for solving $f(x) = ax^2 + bx + ...
0
votes
5answers
35 views

Smallest value of function on a line

Problem : If the point $(\alpha, \beta)$ lies on the line $2x+3y=6$, the smallest value of $\alpha^2+\beta^2$ is (a) $36/13$ (b) $6\sqrt{13}/13$ (c) $6$ (d) $13$ Solution : Since ...
2
votes
5answers
190 views

Show that this expression is a perfect square?

Show that this expression is a perfect square? $(b^2 + 3a^2 )^2 - 4 ab*(2b^2 - ab - 6a^2)$
6
votes
2answers
88 views

Why/when did these extraneous solutions appear while solving a quadratic equation?

I am trying to solve the quadratic equation $x^2 + x + 1 = 0$. $x^2 = -1 - x $ $\iff x = -\frac{1}{x} - 1$, assuming $x\neq 0$. Substituting that into the original equation gives $x^2 + (-\frac{1}{x} ...
2
votes
4answers
52 views

What is a complex constant and how do I use it?

I have a question I am trying to understand: "Let $b$ and $c$ be complex constants such that $z^2+bz+c=0$ has two different real roots. Show that $b$ and $c$ are real." My biggest problem here is ...
1
vote
0answers
39 views

Quadratic Congruence in $\mathbb Z/2^n \mathbb Z$

Given the congruence $ax^2+bx+c \equiv 0 \pmod {2^n}$, how precisely does one go about finding its roots? I'm comfortable with quadratic congruence mod n with n odd, but 2's lack of a multiplicative ...
1
vote
3answers
41 views

How do I solve: $6(x^2+2)<17x$

How do I solve this kinds of inequality. I can do it if all the 'x' is in one side. However, this one have x at both sides of the equation. And we don't know whether it's a positive or negative value. ...
3
votes
1answer
65 views

Solution to a System of Quadratic Equations

Problem: Solve for the values of a, b Equation 1: $$(x_1-a)^2+(y_1-b)=r^2$$ Equation 2: $$(x_2-a)^2+(y_2-b)^2=r^2$$ Where, $x_1, x_2, y_1, y_2$ and $r$ are all constant values For the ...
2
votes
2answers
24 views

How to implement a numerically stable solution of a quadratic equation?

Solving $a x^2 + bx +c=0$ for $x$ gives $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ for $a \ne 0$. But for $a = 0$ we get $x=-\frac{c}{b}$. How to implement a numerically stable algorithm computing ...
1
vote
1answer
65 views

How to solve $\frac{2x+1}{2x-3}+\frac{7x\:}{9-4x^2}=1+\frac{x-4}{2x+3}$ for $x$?

Can somebody explain me this one! $\frac{2x+1}{2x-3}+\frac{7x\:}{9-4x^2}=1+\frac{x-4}{2x+3}$ My book says the answer is $x_1 = 0$; $x_2 = 6$. I tried to solve it and got stuck somewhere in: ...
0
votes
1answer
28 views

How to obtain root of this quadratic equation

I got this quadratic equation in a problem $T^2 - 2T - 40 = 0$, but i am unable to find the roots of this equation. Is any other concept hidden in this equation? Please help. I am basically a Bipc ...
2
votes
3answers
41 views

can i solve this quadratic equation this way

I was basically doing a physics problem and came across this equation in midway $\dfrac{2n-1}{n^2} = \dfrac{11}{36}$ then I equated $2n-1 = 11$ and $n^2 = 36$ and the value of $n$ which I got is ...
0
votes
1answer
72 views

I am having problems with this system of equations [closed]

Hello guys im trying to work out the follow system with no success: $$\left\{\begin{array}{rcl}x+2y&=& 6 \\3x^2-xy+4y^2&=&48\end{array}\right. $$ why? thanks. I tried to solve it ...
0
votes
2answers
34 views

quadratic equation question

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. the distance travelled before it reached the ground is as follows... s = Uot + 1/5gt2 where Uo ...
1
vote
2answers
58 views

Finding the probability an equation has real roots.

If $Q$~UNIF$(0,3)$, find the probability that the roots of the equation $g(t)=0$ are real, where $g(t)=4t^2+4Qt+Q+2$. There was a similar question asked that I looked at, but I am still a little ...
0
votes
5answers
50 views

Solving a quadratic trigonometric equation?

The equation is $6 \cos^2x+\cos x=1$, My work: $6x^2+x-1=0$ $(3x-1)(2x+1)$ $3x-1=0 ∨ 2x+1=0$ $x=\frac{1}{3} ∨ x= \frac{-1}{2}$ But I do not know how to progress further.
0
votes
0answers
23 views

A question using quadratic equations.

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. the distance travelled before it reached the ground is as follows... s = Uot + 1/5gt2 where Uo ...
0
votes
3answers
52 views

Using sum/product of quadratic roots to solve cubic equation

Given $\alpha$ and $\beta$ are the roots of the quadratic equation $6x^2 + 2x - 3 = 0$, how do I find the value of: $$ \alpha^3 + \beta^3 $$ and: $$ \frac{1}{\alpha^3} + \frac{1}{\beta^3} $$ ...
1
vote
5answers
85 views

Distribution of integer solution pairs (x,y) for $2x^2 = y^2 + y$

I am looking for integer pairs $(x,y)$ that respect $$2x^2 = y^2 + y$$ For example $(6,8)$ is a solution for that. Simple solution is to enumerate on $x$ or $y$ and test if the corresponding ...
0
votes
1answer
31 views

Find domain of function with quadratic numerator algebraically

I'm stuck on this problem: $$f(x) = \frac{x^2 -4}{x}$$ I need to determine why this function's domain is not: $$\{x|x \neq \pm 2\}$$ All of the examples that I've seen have the quadratic in the ...
0
votes
2answers
33 views

How to prove one of these equations has real roots?

Question: If $\;a,\, b,\, c,\, d \;$ are real and $\;ac = 2( b + d) $ ,then show that at least one of the equations: $\; x^2 + ax + b = 0 \;$ and $\; x^2 + cx + d = 0 \;$ has real roots. I've ...
1
vote
2answers
269 views

Solving inequalities, simplifying radicals, and factoring. (Pre calculus)

(Q.1) Solve for $x$ in $x^3 - 5x > 4x^2$ its a question in pre calculus for dummies workbook, chapter 2. The answer says: then factor the quadratic: $x(x-5)(x+1)>0$. Set your factors equal to ...
0
votes
3answers
35 views

Quadratics with unknowns

If $5x^2 – t = 4x$, and $x$ and $t$ are both positive real numbers. What is $x$ equal to? How do you find $x$? Is there a specific formula?
0
votes
1answer
19 views

Quadratic factor to complex numbers

How to convert this quadratic factor to complex number form? (With steps please) Reference: $Z = a + bi$, $i = \sqrt{-1}$ $$-3 + \frac{\sqrt{-12}}{2}$$ Thanks!
0
votes
0answers
17 views

system of two quadratic equations with two variables

Is there a general way to solve exactly a system of this shape (the $a_i$ are constants): $$\begin{array}{cc}a_1x^2+a_2x+a_3y^2+a_4y+a_5=0\\ a_6xy+a_7x+a_8y+a_9=0 \end{array} $$ It comes from a ...
1
vote
1answer
97 views

When is $(x+3)^2$ equal to $x^2 +9$?

http://matheducators.stackexchange.com/a/1400/775 Someone commented that the equation in the above answer might sometimes be correct after I commented a correction (feel free to rewrite it ...
2
votes
1answer
51 views

Nonlinear first order ODE with quadratic in the derivative

This equation shouldn't be so hard, and yet I'm stymied. $$ \left( \frac{dw}{dz} \right )^2 + \alpha \frac{dw}{dz} + w \beta = 0 $$ with $w(0) = w_0>0$ $w(L) = 0$ for some known L and ...
0
votes
1answer
17 views

system of equations solving with only that information

Hi would would I go around to solve the following, there is no other information stat is given other than the fact that i have already expanded this from this $(25-y)(x+8)=523$ $25x-8y=323$
0
votes
1answer
54 views

Type of this Conic section

I want to determine, to which type the following Conic sections belong to: $$ \begin{align} \textrm{(i)}&\quad-8x^2+12xy-6x+8y^2-18y+8=0\\ \textrm{(ii)}&\quad5x^2-8xy+2x+5y^2+2y+1=0 ...
0
votes
4answers
39 views

Finding the three unknowns

Can someone show me the steps to finding the three unknowns of these two equations. $$-a-bx+cx^2 = x^2+2x+1$$ The answers are $a=\ ...\ $, $b=\ ...\ $, and $c=\ ...$ , but I can't see how they ...
0
votes
1answer
25 views

Find roots of binomial expression by replacing some variables?

So we have the binomial expression * I might be not using the correct term,english isnt my first language* $$ \left[1- \frac 34e^{-j2\pi\cdot f} + \frac 18e^{-j4\pi \cdot f} \right]$$ How do I find ...
0
votes
1answer
44 views

Homework: canonical form of quadratic form

X=(x,y,z) Q(X) = $x^2 + 4xy + 6xz + 3y^2 +8yz +5z^2 $ I got by using completing the square method: Q(X) = $(x+2y+3z)^2 - (y+2z)^2$ so as I learned now I do: $u = x+2y+3z$ $v = y+2z$ $w = 0 $ ...
1
vote
4answers
134 views

How can I solve equation $x^2 - y^2 -2xy - x + y = 0$?

I have this equation with 2 variables - $$x^2 - y^2 -2xy - x + y = 0$$ The only condition I have is that $x + y$ should be greater than $10^{12}$. EDIT - I need $x$ and $y$ to be integer. I ...
2
votes
1answer
44 views

Calculate the volume of water in glass over time.

For A) I found that volume should be defined by But I got no idea what to do in b) and c)
1
vote
0answers
49 views

Showing DO NOT exist GCD of $6$ and $2+2 \sqrt{-5}$ in $\Bbb Z[\sqrt{-5}]$.

Showing DO NOT exist gcd of $6$ and $2+2 \sqrt{-5}$ in $\Bbb Z[\sqrt{-5}]$. I tried it. Suppose $d$ is GCD of $6$ and $2+2 \sqrt(-5)$. then there exist $x,y \in \Bbb ...
0
votes
1answer
71 views

Find pressure in a sinusoidal function

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with laughing gas. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 ...
2
votes
1answer
62 views

Expanding Square Roots, Why No Negative?

I haven't thought through algebra in a while and the last explanation I received of this seemed arbitrary. I hope I can get some clarification here. I understand that $\sqrt{+a} = \pm b$. Here's ...
4
votes
7answers
88 views

How to find $x^2 - x$?

I'm quite a novice when it comes to maths. I'm on a problem in which I have had to isolate $x$ , through factorials which I completed without problem. However, now I am stuck on a seemingly more minor ...
-1
votes
2answers
37 views

Proof of axis of symmetry equation [closed]

Because quadratic functions are symmetrical how do you prove the axis of symmetry equation. $x=(-b/(2a))$
0
votes
1answer
27 views

Proof of axis of symmetry [duplicate]

How do you prove -b/2a the Axis of symmetry equation using the Quadratic formula?
0
votes
2answers
36 views

What are the parameters of a parabola

In the following figure I understand the $bx+c$ part. It is simply the equation of a line. But I don't understand where did $ax^2$ came from? What exactly is it? What does $a$ tell us about a ...
1
vote
1answer
236 views

Show that that if $p,q,r,s$ are real numbers and $pr=2(q+s)$, then at least one of the eqns $x^2+px+q=0$ and $x^2+rx+s=0$ has real roots.

Show that that if $p,q,r,s$ are real numbers and $pr=2(q+s)$, then at least one of the eqns $x^2+px+q=0$ and $x^2+rx+s=0$ has real roots. My Attempt to the solution we know to have a real solution ...
1
vote
2answers
42 views

Find maximum of a system of equations

You have 300 meters of fencing with which to build two enclosures. One will be a square, and the other will be a rectangle where the length of the base is exactly twice the length of the height. (a) ...
6
votes
3answers
89 views

Solve $x^{3}-3x=\sqrt{x+2}$

Solve for real $x$ $$x^{3}-3x=\sqrt{x+2}$$ By inspection, $x=2$ is a root of this equation. So, I squared both sides and divided the six degree polynomial obtained by $x-2$. Then I got a ...
0
votes
5answers
48 views

How do you factor a quadratic expression, without using the formula?

I am asked to factor $2x^2 -3x+1=0 $ using factorization, but I run into fractions, and it becomes very messy and complicated to deal with, especially since specifically asked not to use the formula. ...
3
votes
3answers
207 views

Algebraic Relationships - Quadratic Equations

I am having a tough time with the following question: If $x$ is real and $p=3(x^2 + 1)/(2x-1)$, then prove that $p^2 - 3(p+1)\geq 0$. I don't know how to tackle this question. Thanks for your ...