Question

In each of the following two polynomials, find the value of a, if x + a is a factor. (i) x² + ax² - 2x + a + 4 (ii) x¹-a²x² + 3x - a​

Answer 1

Answer:

Let f(x)=x

3

+ax

2

−2x+a+4 be the given polynomial.

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

∴ f(−a)=0

⇒ (−a)

3

+a(−a)

2

−2(−a)+a+4=0

⇒ −a

3

+a

3

+2a+a+4=0

⇒ 3a=−4

⇒ a=

3

−4