Question

If 3 is one zero of the polynomial f(x) = 9x² - 3(a - 1)x + 5, then the value of a is​

Answer 1

Answer:

a = 95/9

Step-by-step explanation:

If 3 is a zero of f(x) this means that 3 = x in this polynomial

we know that f(x) = 0

So,

    9x² - 3(a-1)x+5 = 0

replacing x with 3

    9(3)² - 3(a - 1)3 + 5 = 0

81 -9a + 9 + 5 = 0

95 - 9a = 0

95 = 9a

95/9 = a

Answer 2

Given:

A polynomial equation f(x) = 9x² - 3(a - 1)x + 5, where 3 is one of the two zeroes of the polynomial.

To Find:

The value of a.

Solution:

The given question can be solved by using the concepts of quadratic equations.

1. It is given that 3 is a root of the polynomial f(x) = 9x² - 3(a - 1)x + 5.

2. Consider a quadratic equation ax² + b x + c = 0 with roots as p,q. According to the concepts of quadratic equations, when p and q are substituted in the given quadratic equation the value equals 0,=> ap² + bp + c =0 and aq² +bq + c = 0.

3. From the above properties the value of a can be calculated,

=> 9(3)² -3(a-1)3 + 5 = 0,

=> 9 x 9 -9(a-1) + 5 = 0,

=> 81 - 9a + 9 + 5 = 0,

=> 9a = 95,

=> a = 95/9.

Therefore, the value of a is 95/9.