Question

If 1 and -3 are zeros of polynomial p(x)=x³ -ax^​2-13x+b find the values of a and b.

Answer 1

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