# If 1 is the Zero of the Polynomial p(x) = ax² – 3(a – 1) x – 1, Then Find the Value of a.

By BYJU'S Exam Prep

Updated on: October 17th, 2023

If 1 is the zero of the polynomial p(x) = ax² – 3(a – 1) x – 1, then find the value of a

The steps to find the value of a for the polynomial p(x) = ax² – 3(a – 1) x – 1 are shown below:

• Substitute the zero value into the polynomial equation: p(1) = a(1)² – 3(a – 1)(1) – 1.
• Simplify the equation: a – 3(a – 1) – 1 = 0.
• Expand and simplify further: a – 3a + 3 – 1 = 0.
• Combine like terms: -2a + 2 = 0.
• Solve for ‘a’ by isolating the variable: -2a = -2.
• Divide both sides of the equation by -2: a = -2 / -2.
• Simplify the expression: a = 1.

## If 1 is the Zero of the Polynomial p(x) = ax² – 3(a – 1) x – 1, Then Find the Value of a

Solution:

To find the value of ‘a’ if 1 is a zero of the polynomial p(x) = ax² – 3(a – 1)x – 1, we can use the fact that a zero of a polynomial is a value of ‘x’ for which the polynomial evaluates to zero.

Given that 1 is a zero of the polynomial, we substitute x = 1 into the polynomial equation and set it equal to zero:

p(1) = a(1)² – 3(a – 1)(1) – 1 = 0

Simplifying the equation:

a – 3(a – 1) – 1 = 0

a – 3a + 3 – 1 = 0

-2a + 2 = 0

Now, we solve for ‘a’:

-2a = -2 a = -2 / -2

a = 1

Therefore, the value of ‘a’ is 1.