Question

If x = 2 and x = 0 are roots of thr polynomial f (x) = 2x³ - 5x² + ax + b. Find the values of a and b.​

Answer 1

Given polynomial is p(x) = 2x3-5x2+px+b

Since x = 2 is zero of the given polynomial, we have p(2) = 0

Now put x = 2 in p(x)

p(2) = 2(2)3 – 5(2)2 + p(2) + b

⇒ 0 = 16 – 20 + 2p + b  

⇒ 2p + b = 4 → (1)

It is also given that x = 0 is also a zero of the given polynomial

Hence p(0) = 0

Put x = 0 in p(x), we get

p(0) =  2(0)3 – 5(0)2 + p(0) + b

⇒ 0 = 0 – 0 + 0 + b  

∴ b = 0

Put b = 0 in (1), we get

2p + 0 = 4

∴ p = 2