Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [quadratics]

Questions about quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

Questions about quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

The root of $y=ax^2+bx+c$ can be solved by the formula $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

5400 questions
1
vote
2 answers

Two quadratic equations, more than two solutions?

It's clear that a system of two quadratic equations can have none, one or two solutions. For example: $y = x^2 + 2$ and $y = - x^2 + 1$ have none. $y = x^2$, $2x^2 - 8x + 8$ and $y = - x^2 + 8x - 8$ have $4$ as common solution. And $2x^2 - 8x + 8 =…
Quora Feans
  • 1,059
1
vote
4 answers

When do you use the quadratic formula?

I am revising for a mathematics exam and am looking over simultaneous equations. I was curious as to when I use the quadratic formula and when I don't? I realize there are multiple ways to solve a question - for example 2x^2+7x-15=0 - can I use the…
Harry Kitchener
  • 175
1
vote
2 answers

Sum of complex roots of quadratic equation.

How to find the sum of the complex roots of the quadratic equation $$px^2+qx+r=0$$ if $r>p>0$, and $p,q,r \in\mathbb R$ ?
user140013
  • 13
1
vote
0 answers

Variable quadratic functions

I have some doubts in proving the following:- C is the curve $$y = \frac 1 {k+1} [2x^2 + (k + 7)x + 4]$$, where k is a real number not equal to -1. Show that C always passes through two fixed points for all allowable values of k. (What are the…
Mick
  • 17,141
1
vote
3 answers

Solving a quadratic using vietas theorem I keep going in circles.

I am trying to solve the quadratic equation $x^2-48x+432=0$ with out directly factoring OR using the quadratic equation. I am going with vieta. So $$r+s=48$$ and $$rs=432$$ I've already solved it by plugging in factors of $432$ the roots are $$r=12,…
Chris
  • 643
1
vote
2 answers

Reducing quartic equations to quadratic

I'm trying to re-learn basic math/algebra, and I can't get passed one question concerned with reducing quartic equation to a quadratic: Find, correct to 3 significant figures, all the roots of the equation $8x^4 - 8x^2 + 1 = \frac12\sqrt 3$ I've…
hohner
  • 1,049
1
vote
2 answers

Rearranging quadratic equations

I have an equation I'd like to rearrange that I'm having trouble with: The equation goes: $$r = 2ut - 0.333(2ut)^2$$ (on a computer I enter (2*u)*t - (0.333*((2*u)*t))^2 to make sure the order of operations done by the computer is correct. However…
SJWard
  • 135
1
vote
2 answers

Query about a statement on the consequence of two quadratic equations having a common root

I have read an answer (in this site, but I lost the question number) saying something like the following:- If the quadratic equations F(x) = 0 and f(x) = 0 have a common root, then the quadratics are proportional to each other. That is, K[f(x)] =…
Mick
  • 17,141
1
vote
0 answers

Calculating $(x_1^{x_2})(x_2^{x_1})$ in a quadratic equation

Supposing $S=x_1+x_2$ and $P=x_1x_2$ where $x_1$ and $x_2$ are the roots of the quadratic equation $ax^2+bx+c=0$ (it's clear the equation is equivalent to $x^2-Sx+P=0$ where $S=-b/a$ and $P=c/a$), how we can calculate $(x_1^{x_2})(x_2^{x_1})$?
user112023
  • 11
1
vote
3 answers

Prove that if $ac + bc + c^2 < 0$ then equation (usual notation) has two roots

We have $a, b, c$ real parameters, $a ≠ 0$. Prove that $ax^2 + bx + c = 0$ has two different roots ($b^2-4ac > 0$), if $ac + bc + c^2 < 0$
Gabor Magyar
  • 147
1
vote
2 answers

Least Value of the Quadratic Expression

What is the least value of this expression? Please show me a way to determine it.
Tejas
  • 2,082
1
vote
1 answer

Solving Quadratics

A rectangular lawn measures 30 m by 40 m. Jason is cutting the lawn from the outside perimeter in toward the centre by cutting strips along the entire perimeter first, then continuing as he cuts toward the centre. How wide is the strip that has been…
Rose
  • 515
1
vote
2 answers

Result of non-negativity condition

Consider the non-negativity condition $f(t) = t^2 {\Vert v \Vert}^2 - 2 t \langle u , v \rangle + {\Vert u \Vert}^2 \geq 0$. Where $u$ and $v$ are vectors, and $t$ being a real scalar. In the process of proving the Cauchy-Schwarz Inequality, one…
Celestine
  • 13
1
vote
0 answers

Let $f(x)=ax^2 + bx + c$. Suppose $f(x)=x$ has no real roots. Show that the equation $f(f(x))=x$ has also no real solutions.

Let $f(x)=ax^2 + bx + c$. Suppose $f(x)=x$ has no real roots. Show that the equation $f(f(x))=x$ has also no real solutions. One of the solution found on this site goes like this: Since $f$ is continuous, saying that $f(x) = x$ has no solution…
zaemon_23
  • 465
1
vote
1 answer

Quadratic Equation with 2 Variables

I have this Equation : $xy + y^2 = 19 + 2x^2$ I need to find every $(x , y)$ where $x$ and $y$ are integers. I first tried to solve it by dividing everything by $y^2$ , but $19$ creates a problem , because we will get term $19/y^2$ , which is…
NikoMolecule
  • 65
1 2 3
…
64 65