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.
Table of content
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.
Answer:
If 1 is the Zero of the Polynomial p(x) = ax² – 3(a – 1) x – 1, Then the Value of a is 1
Similar Questions:
- If α and β are Zeros of Polynomial x²+6x+9, then Form a Quadratic Polynomial whose Zeros are -alpha, -beta.
- If sum of the Zeros of the Polynomial Ky^2+2y-3K is Twice their product of Zeros then Find the Value of K
- If α and β are the Zeros of the Polynomial f(x)=x^2+x−2, Find the Value of (1/α−1/β)
- P(x)=x2 + 2(√2)x – 6 Find the Zero of the Polynomial and Verify between Zero and Coefficients
- If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x^2 − 5x − 1, Find the Value of α^2β + αβ^2
