Question

if the roots of a quadratic equation are -2 and 3, the equation can be written as
a. (x - 2)(x + 3) = 0
b. (x + 2)(x - 3) = 0
c. (x + 2)(x + 3) = 0
d. (x - 2)(x - 3) = 0

Explanation:

Step1: Recall root to factor rule

If $r$ is a root, then $(x-r)$ is a factor.

Step2: Create factors for given roots

For root $-2$: $(x - (-2)) = (x+2)$
For root $3$: $(x - 3)$

Step3: Form the quadratic equation

Multiply the factors and set to 0: $(x+2)(x-3)=0$

Answer:

B. $(x + 2)(x - 3) = 0$