Question

write a quadratic equation for each condition below. explain your reasoning.
a. the equation has solutions that are opposites.
b. the equation has two solutions.

a. which of the following quadratic equations has solutions that are opposites?
a. $x^2 - 4 = 0$
b. $x^2 + 4x - 12 = 0$
c. $x^2 + 4x + 4 = 0$
d. $x^2 - 4x + 4 = 0$

Explanation:

Step1: Recall sum of roots rule

For quadratic $ax^2+bx+c=0$, sum of roots is $-\frac{b}{a}$.

Step2: Opposite roots sum to 0

Set $-\frac{b}{a}=0$, so $b=0$.

Step3: Check options for $b=0$

Only Option A has $b=0$.

Step4: Verify roots of Option A

Solve $x^2-4=0$: $x^2=4$, so $x=2$ and $x=-2$, which are opposites.

Answer:

A. $x^2 - 4 = 0$