x3 + 2x2 + ax + b is exactly divisible by (x2 – 1). The values of a

1.	x3 + 2x2 + ax + b is exactly divisible by (x2 – 1). The values of a and b is ……………… A) a = -1, b = 2B) a = 1, b = -2C) a = 1, b = 2D) a = -1, b = -2
Answer» Correct option is (D) a = -1, b = -2 (x - 1) and (x + 1) are factors of \((x^3+2x^2+ax+b).\) \(\Rightarrow\) x = 1 and x = -1 are zeros of \((x^3+2x^2+ax+b).\) \(\therefore\) 1+2+a+b = 0 and -1+2-a+b = 0 \(\Rightarrow\) a+b = -3 and a - b = 1 \(\Rightarrow\) (a+b) + (a - b) = -3+1 \(\Rightarrow\) 2a = -2 \(\Rightarrow\) a = \(\frac{-2}2\) = -1 Then b = - 3 - a = -3 - (-1) = -3+1 = -2 Correct option is D) a = -1, b = -2

x3 + 2x2 + ax + b is exactly divisible by (x2 – 1). The values of a and b is ……………… A) a = -1, b = 2B) a = 1, b = -2C) a = 1, b = 2D) a = -1, b = -2

Answer»

Correct option is (D) a = -1, b = -2

(x - 1) and (x + 1) are factors of \((x^3+2x^2+ax+b).\)

\(\Rightarrow\) x = 1 and x = -1 are zeros of \((x^3+2x^2+ax+b).\)

\(\therefore\) 1+2+a+b = 0 and -1+2-a+b = 0

\(\Rightarrow\) a+b = -3 and a - b = 1

\(\Rightarrow\) (a+b) + (a - b) = -3+1

\(\Rightarrow\) 2a = -2

\(\Rightarrow\) a = \(\frac{-2}2\) = -1

Then b = - 3 - a = -3 - (-1)

= -3+1 = -2

Correct option is D) a = -1, b = -2