Question

find the value of a , if x-a is a factor of
${x}^{3} - {ax}^{2} + 2x + a - 1$

Answer 1

Zero of ( x - a ) =  0

             x = a.

By Factor theorem ,

p ( x ) = x³ - ax² + 2x + a - 1

p ( a ) = ( a)³ - a (a²) +2a + a - 1 = 0

         ⇒ a³ - a³  +2a+ a - 1 = 0

         ⇒ 3a - 1 = 0

        ⇒ a = 1/3.

So, the value of a is 1/3.