Question

If x-2 is a factor of x3-2ax2 + ax-1,then find the value of a

Answer 1

Step-by-step explanation:

⇒ Sub x = 2 into the polynomial will return us 0

Sub x = 2 into x³ - 2ax² + ax - 1

(2)³ - 2a(2)² + 2a - 1 = 0

8 - 8a + 2a - 1 = 0

7 - 6a = 0

6a = 7

a = 7/6

Answer: a = 7/6

Answer 2

Given,

x - 2 is a factor of x³- 2ax² + ax - 1

To find,

The value of a

Solution,

Since, x - 2 is a factor of x³- 2ax² + ax - 1 , then x = 2 completely satisfy the given equation.

x³- 2ax² + ax - 1 = 0

Now, let us substitute x = 2 in the above equation.

⇒   (2)³- 2a(2)² + a(2) - 1 = 0

⇒   8 - 8a + 2a - 1 = 0

⇒   7 - 6a = 0

- 6a which is on the left-hand side of the equation would shift to the right-hand side of the equation and its sign would change from -6a to +6a.

⇒   7 = 6a

⇒   a = 7/6

Hence, the value of a = 7/6 such that x - 2 is a factor of x³- 2ax² + ax - 1.