New posts in quadratics

Proving that $\cos\frac{2\pi}{13}+\cos\frac{6\pi}{13}+\cos\frac{8\pi}{13}=\frac{\sqrt{13}-1}{4}$

algebra-precalculus trigonometry quadratics substitution

If $3x^2 -2x+7=0$ then $\left(x-\frac{1}{3}\right)^2 =$?

algebra-precalculus quadratics completing-the-square

Find all integer solutions of: $\;\frac{1}{m}+\frac{1}{n}-\frac{1}{mn^2}=\frac{3}{4}$

number-theory contest-math quadratics

A monic quadratic trinomial $P(x)$ is such that $P(P(P(x)))=0$ and $P(x)$ have a common root

algebra-precalculus polynomials roots quadratics

$(x^2+2mx+7m-12)(4x^2-4mx+5m-6)=0$ have two distinct real roots

algebra-precalculus quadratics

A polynomial with integer coefficients that attains the value $5$ at four distinct points

algebra-precalculus polynomials quadratics integers

Factoring $2k^{2} + 7k + 6$

algebra-precalculus quadratics factoring

Are all quadratics factorable into a product of two binomials?

algebra-precalculus polynomials quadratics

How do I solve a quadratic for $k$ using the discriminant

quadratics discriminant

What is the connection between the discriminant of a quadratic and the distance formula?

algebra-precalculus quadratics

Set f(x) = $x^2 + ax + b$. Prove max{$|f(-1)|, |f(0)|, |f(1)|$} $\geq$ $\frac12$

real-analysis quadratics maxima-minima absolute-value

Let f(x) = $x^2+ax+b,a,b \in R$. If $f(1)+f(2)+f(3)=0$, then the nature of the roots of the equation $f(x) =0$ is .....

algebra-precalculus polynomials quadratics

One root of $x^2 + px + q = 0$, for $p, q$ real, is $x = 2 + 3i$. How do you find $p$ and $q$?

complex-numbers solution-verification quadratics

Cartesian equation of uniformly accelerated motion

geometry quadratics parametric conic-sections kinematics

Quadratic equation with multiple parameter

algebra-precalculus quadratics

Finding the largest $c$ such that $4.7(x-c) = 9-\frac12x^2$ has a real solution $x$

algebra-precalculus inequality quadratics

What is the sum of the squares of the roots of the equation $x^2 − 7[x] + 5 = 0?$ (Here $[x]$ denotes the greatest integer less than or equal to $x$)

Find $C$ such that $x^2 - 47x - C = 0$ has integer roots, and further conditions

quadratics prime-factorization

Proving the second root of a quadratic equation

For any odd prime $p$, a quadratic is solvable mod $p^2$ if it is solvable mod $p$, and $p$ does not divide the discriminant and leading coefficient.

elementary-number-theory modular-arithmetic quadratics