Question

If -1 is a zero polynomial p(x) = ax^3 - x^2 + x + 4, then find the value of 'a'
With Explanation

Answer 1

Answer:

The required value of a is 2.

Step-by-step explanation:

Given :

-1 is a zero polynomial p(x) = ax³ - x² + x + 4

To find :

the value of a

Solution :

If 'a' is a zero of the polynomial p(x), then p(a) = 0

As -1 is a zero of the given polynomial, if we put x = -1 the result is zero.

Put x = -1,

p(-1) = 0

a(-1)³ - (-1)² + (-1) + 4 = 0

a(-1) - 1 - 1 + 4 = 0

-a - 2 + 4 = 0

-a + 2 = 0

 a = 2

∴ The value of a is 2

Verification :

Put a = 2 and x = -1 and check if the result is zero.

⇒ (2)(-1)³ - (-1)² + (-1) + 4

⇒ 2(-1) - (1) - 1 + 4

⇒ -2 - 1 - 1 + 4

⇒ -4 + 4

⇒ 0

So, the value of a is 2.