Question

If 1 and -3 are zeroes of the polynomial p(x)=x^3-ax^2-13x+b, find the values of a and b.

Answer 1

Substitute x = 1

1 - a - 13 + b = 0

a - b = - 12

Substitute x = -3

-27 - 9a + 39 + b = 0

-9a + b = -12


a = 3 and b = 15

Answer 2

Hey

Here is your answer,

Let p(x) = x 3 – ax 2 – 13x + b

Now, p(1) = 0

(1)3 – a(1)2 –13(1) + b = 0

⇒ –a + b = 12 .....(1)

Now, , p(– 3) = 0

⇒ (– 3)3 – a (– 3)2 – 13(– 3) + b = 0

⇒ 9a – b = 12 .....(2)

Adding, equation (1) and (2),

8a = 24

⇒ a = 3

b = 12 + 3 = 15 (Using equation (1))

∴ a = 12 and b = 15

Hope it helps you!