Question

if 2 is a zero of polynomial f(x)=ax²-3(a-1)x-1;then find the value of a

Answer 1

the..f(2)=a(2)^2-3a+1(x-1)
=4a-3a+2-1
=a+1
a=-1.

Answer 2

Given 2 is a zero of polynomial f(x).

So, x = 2.

By Factor theorem,

f(x) = ax² - 3 ( a - 1 )x - 1

f(2) = a(2)² - 3( a - 1 )2 - 1 = 0

     ⇒ 4a - ( 3a - 3 )2 - 1 = 0

    ⇒ 4a - 6a + 6 - 1 = 0

    ⇒ -2a + 5 = 0

   ⇒ -2a = -5

   ⇒ a = -5 / -2

   ⇒ a = 5 / 2

So, if the value of a is 5/2 then 2 will be a zero of f(x).