Find a quadratic equation with integer coefficients that has the given solution set.
-$\left\{-4, \frac{9}{4}\right\}$
A) $4 x^{2}+7 x-36=0$
B) $4 x^{2}+11 x+36=0$
C) $4 x^{2}-7 x-36=0$
D) $x^{2}-7 x-36=0$

Question

Quizplus · Accepted Answer

Given the roots $-4$ and $\frac{9}{4}$, the sum of the roots is $-4 + \frac{9}{4} = -\frac{7}{4}$ and the product of the roots is $-4 \times \frac{9}{4} = -9$. The quadratic equation in the form $ax^2 + bx + c = 0$ can be found using the sum and product of roots formula: $b/a = -(\text{sum of roots})$ and $c/a = \text{product of roots}$. Multiplying through by 4 to ensure integer coefficients, we get $4x^2 + 7x - 36 = 0$, which matches option A.

Find a Quadratic Equation with Integer Coefficients That Has the Given