Question

If x − 2 is a factor of the following two polynomials, find the values of a in each case x³ − 2ax² + ax − 1.

Answer 1

 Let  `f(x) = x^3 - 2ax^2 + ax - 1` be the given polynomial.

By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0

Therefore,

`f(2) = (2)^3  - 2a(2)^2 a(2) - 1 = 0`

                         `8-8a + 2a - 1 = 0`

                                       `-6a + 7 = 0`

                                                     `a = 7/6`

Thus the value of a is 7/6.