Question

If x-2 is a factor of x2-3x+5 a then the value of a

Answer 1

The polynomial given is a quadratic polynomial since the degree or the highest power of the polynomial is 2 .

Let f(x) be a function such that f(x) = x² - 3 x + 5 a .

By factor theorem we already know that if x - a if a factor of a function f(x) then x - a = 0 .

Using the factor theorem we can say that x - 2 = 0 .

⇒ x = 2

Putting this value of x in the function we get :

⇒ (2)² - 3(2)² + 5 a = 0

⇒ 4 - 3×4 + 5 a = 0

⇒ 4 - 12 + 5 a = 0

⇒ 5 a = 8

⇒ a = 8/5

The value of a is 8/5 .

NOTE :

Whenever any other factor is given , say x² + 3 x + 2 . Then we need to solve the factor first .

If such a factor exists for f(x) then we can write x² + 3 x + 2 = 0

⇒ x² + 2 x + x + 2 = 0

⇒ x(x + 2) + 1(x + 2) = 0

⇒ (x + 1 )(x + 2) = 0

x = - 1 , - 2

So there are 2 values of x which we can put in the equation .

In such a case we should consider both values .

Answer 2

Answer:

1. if x=2,than value of xsquer-3x+5