Question

Find the value of a for which (x-a) is a factor of a polynomial f(x) = x^5-a^2x^3+2x+a-3

Answer 1

Given,

(x - a) is a factor of polynomial

and f(x) = 0 i.e., (x - a) is a factor of f(x)

$f(x) = {x}^{5} - {a}^{2} {x}^{3} \\ + 2x + a - 3 = 0$

given,
as x - a = 0
=> x = a

substituting the values,

$f(a) = (a) {}^{5} - a {}^{2}(a) {}^{3} + 2(a) \\ + a - 3 = 0$

=> 2a + a - 3 = 0
=> 3a = 0 +3
=> 3a = 3
=> a = 1

Thus,
the value of a is 1

Answer 2

heya...

Here is your answer....