Find the roots of each equation: 4x^3-10x^2-24x=0 #pleaseanswerASAP

Question

Please show step by step how to factor and the final answer.

Answer 1

The polynomial is 4x^3 - 10x^2 - 24x = 0.

Common out x from the polynomial.

x(4x^2 - 10x - 24) = 0

Apply zero product property.

x =0  and  4x^2 - 10x - 24 = 0

Divide the equation 4x^2 - 10x - 24 = 0 by 2.

2x^2 - 5x - 12 = 0

By factoring by grouping.

2x^2 - 8x + 3x - 12 = 0

2x(x - 4) + 3(x - 4) = 0

Factor : (x - 4)(2x + 3) = 0

Again apply zero product property.

x - 4 = 0  and  2x + 3 = 0

x = 4  and  x = - 3/2.

Therefore, the roots of the given polynomial is x = - 3/2, x = 0, and x = 4.