Question

Find the value of 'a' for which (x-1) is a factor of the polynomial a²x³-4ax+4a-1

Answer 1

Answer:

The value of a is ± 1.

Step-by-step-explanation:

The given polynomial is a²x³ - 4ax + 4a - 1.

Let the polynomial be P ( x ).

We have given that,

( x - 1 ) is a factor of the given polynomial.

By factor theorem,

If x = 1, P ( x ) = 0

∴ a² ( 1 )³ - 4a * 1 + 4a - 1 = 0

⇒ a² * 1 - 4a + 4a - 1 = 0

⇒ a² - 1 = 0

⇒ ( a + 1 ) ( a - 1 ) = 0

⇒ ( a + 1 ) = 0 OR ( a - 1 ) = 0

⇒ a + 1 = 0 OR a - 1 = 0

⇒ a = - 1 OR a = 1

⇒ a = ± 1

∴ The value of a is ± 1.