Find a quadratic equation with integer coefficients that has the given solution set.
-$$\{ - 8 , - 2 \}$$
A) $x ^ { 2 } + 16 x - 10 = 0$
B) $x ^ { 2 } + 10 x + 16 = 0$
C) $x ^ { 2 } + 16 x + 10 = 0$
D) $x ^ { 2 } - 10 x + 16 = 0$

Question

Quizplus · Accepted Answer

The correct quadratic equation can be found by using the fact that if $\alpha$ and $\beta$ are the roots of a quadratic equation $ax^2 + bx + c = 0$, then the equation can be written as $x^2 - (\alpha + \beta)x + \alpha\beta = 0$. For the given roots $-8$ and $-2$, the sum $\alpha + \beta = -8 - 2 = -10$ and the product $\alpha\beta = (-8)(-2) = 16$. Therefore, the equation is $x^2 - (-10)x + 16 = x^2 + 10x + 16 = 0$, which matches option B.

Find a Quadratic Equation with Integer Coefficients That Has the Given