Vieta's Formula

Which of the following expresses the quadratic equation whose roots are $p$ and $6$ ?

A) $x^2 - 6p x + (6 + p) = 0$
B) $x^2 + 6p x - (6+b) = 0$
C) $x^2 + (6 + p) x - 6p = 0$
D) $x^2 - (6+p) x + 6p = 0$

In the above diagram, $AB$ is a diameter of the circle with radius $21$ and $CD$ intersects $AB$ at point $P.$ Suppose that $\lvert \overline{CP} \rvert =8$ and $\lvert \overline{DP} \rvert=12.$ If the quadratic equation whose two roots are $\lvert \overline{AP} \rvert$ and $\lvert \overline{BP} \rvert$ can be expressed as $x^2+ax+b=0,$ what is the value of $a+b?$

Which of the following expresses the quadratic equation whose roots are $4$ and $-6$ ?

A) $x^2 + 2 x + 24 = 0$
B) $x^2 - 2 x + 24 = 0$
C) $x^2 + 2 x - 24 = 0$
D) $x^2 - 2 x - 24 = 0$

Let $\alpha$ and $\beta$ be the two roots of the quadratic equation $x^2-mx+n=0,$ and $\alpha+\beta$ and $\alpha\beta$ be the two roots of the quadratic equation $x^2-8x+1=0.$ Then what is the value of $m^3+n^3 ?$

Let $\alpha$ and $\beta$ be the two roots of the quadration $x^2-2x-2=0.$ If the quadratic equation whose two roots are $\alpha^3$ and $\beta^3$ can be expressed as $x^2+ax+b=0,$ what is the value of $3ab?$

Concept Quizzes

Challenge Quizzes

Vieta's Formula - Forming Quadratics

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.