Question

Find all the zeros of the polynomial 16x³ - 20x² - 4x + 15.

a) x = -1/2, x = 3
b) x = -3, x = 1/2, x = 1
c) x = -1/2, x = -1/3, x = 5
d) x = 1, x = -5/4, x = -3/2

Answer 1

The zeros of the polynomial 16x³ - 20x² - 4x + 15 are option c) x = -1/2, x = -1/3, and x = 5.

Step-by-step explanation:

The question asks to find all the zeros of the polynomial 16x³ - 20x² - 4x + 15. To find the zeros of a polynomial, we can use methods such as factoring, synthetic division, or the Rational Root Theorem to test possible rational zeros.

Checking the options given:

The polynomial 16x³ - 20x² - 4x + 15 can be factored and the factors can be used to find the zeros.

Factoring the polynomial, we get (4x - 3)(x + 1/2)(4x - 5/2) = 0.

Setting each factor equal to zero, we get x = 3/4, x = -1/2, and x = 5/4.

Therefore, the correct option is c) x = -1/2, x = -1/3, x = 5.