If - 1 is a zero of the polynomial p (x) = ax³ - x² + x + 4, then find the value of 'a'

The answer to your question is a = 2

Step-by-step explanation:

Data

root = - 1

Polynomial p (x) = ax³ - x² + x + 4

Process

If - 1 is a root of the polynomial, then, we must equal the polynomial to zero and substitute - 1 and solve it for a.

1. - Equal to zero

ax³ - x² + x + 4 = 0

2. - Evaluate in - 1

a (-1) ³ - (-1) ² + (-1) + 4 = 0

3. - Simplification

- a - 1 - 1 + 4 = 0

-a + 2 = 0

4.-Solve for a

-a = - 2

a = 2

a = 2

Step-by-step explanation:

-1 is a zero of the polynomial p (x)

means

a (-1) ³ - (-1) ² + (-1) + 4 = 0

means

-a - 1 - 1 + 4 = 0

means

a = 2