Question

Solve the following quadratic by factoring:

n³ −9n=0
a) n=0 and n=9
b) n=0 and n=−9
c) n=3 and n=−3
d) n=3 and n=9

Answer 1

To solve the quadratic equation by factoring, set the equation equal to zero, factor out the common factor, factor the quadratic expression inside the parentheses, and set each factor equal to zero to find the solutions.

Step-by-step explanation:

To solve the given quadratic equation by factoring:
Step 1: Set the equation equal to zero.
n³ − 9n = 0
Step 2: Factor out the common factor, n.
n(n² − 9) = 0
Step 3: Factor the quadratic expression inside the parentheses.
n(n − 3)(n + 3) = 0
Step 4: Set each factor equal to zero and solve for n.
n = 0 or n - 3 = 0 or n + 3 = 0
Thus, the solutions to the quadratic equation are n = 0, n = 3, and n = -3.
Therefore, the correct answer is option (c) n = 3 and n = -3.