Question

In each of the following two polynomials, find the value of a, if x-a is a factor:
(i) x⁶-ax⁵+x⁴-ax³+3x-a+2.
(ii) x⁵-a²x³+2x+a+1.

Answer 1

answer : (i) a = -1 (ii) a = -1/3

(x - a) is a factor of given polynomial.

so, x = a is a root of given polynomial.

Now, (i) x⁶-ax⁵+x⁴-ax³+3x-a+2

putting, x = a

a⁶-a.a⁵+a⁴-a.a³+3a - a+2 = 0

⇒3a - a + 2 = 0

⇒2a + 2 = 0

⇒a = -1

similarly putting x = a in (ii)

we get, a⁵-a².a³+2a+a+1 = 0

⇒2a + a + 1 = 0

⇒3a + 1 = 0

⇒a = -1/3

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