Question

solve ques no.24only plz

Answer 1

I am going to go all the way and find the values of a and b here.

As (x - 1) is a factor of p(x) we have by the factor theorem that p(1) = 0.

Hence, 1^3 - a(1)^2 - 13(1) + b = 0 ⇒ a - b = -12      [1]

Similarly as (x + 3) is a factor of p(x), it follows that p(-3) = 0.

Hence, (-3)^3 - a(-3)^2 - 13(-3) + b = 0 ⇒ 9a - b = 12     [2]

Solving [1] and [2] simultaneously :

[2] - [1] : 8a = 24 ⇒ a = 3.

[1]: 3 - b = -12 ⇒ b = 9.

By the way, equations [1], [2] are the relations between a and b that can be deduced using the given information.