Question

if (x2) and (x-1) are the factors of the polynomial f(x)=x cubeax10x squareb,how to find the values of a and b?

Answer 1

HEY!!

It is given that (x + 2) and (x – 1) are the factors of the polynomial f(x) = x3 + ax +10x2 + b.
Therefore, by factor theorem, f(–2) = 0, f(1) = 0.

f(–2) = 0
⇒ – 8 – 2a + 40+ b = 0
⇒ – 2a + b + 32 = 0 … (1)

f(1) = 0
⇒ 1 + a + 10 + b = 0
⇒ a + b + 11 = 0 … (2)

Now, subtracting equation (2) from (1):
– 2a + b + 32 – (a + b + 11) = 0 – 0
⇒ – 3a + 21 = 0
⇒ 3a = 21
⇒ a = 7

From (2), 7 + b + 11 = 0 ⇒ b = –18

Thus, the values of a and b are respectively 7 and –18.