The value of 6a + 11b if x3 – 6x2 + ax + b is exactly divisible by (

1.	The value of 6a + 11b if x3 – 6x2 + ax + b is exactly divisible by (x2 – 3x + 2) is ………………A) 0 B) 66 C) 132 D) 1
Answer» Correct option is (A) 0 \(\because\) (x - 1) & (x - 2) are factors of \((x^3 – 6x^2 + ax + b)\) \((\because\) (x - 1) (x - 2) \(=x^2-3x+2)\) \(\therefore\) x = 1 and x = 2 are zeros of \((x^3 – 6x^2 + ax + b)\) \(\therefore\) 1-6+a+b = 0 and 8-24+2a+b = 0 \(\Rightarrow\) a+b = 5 and 2a+b = 16 \(\Rightarrow\) (2a+b) - (a+b) = 16 - 5 \(\Rightarrow\) a = 11 \(\therefore\) b = 5 - a = 5 - 11 = -6 \(\therefore\) 6a+11b \(=6\times11+11\times-6\) = 66 - 66 = 0 Correct option is A) 0

The value of 6a + 11b if x3 – 6x2 + ax + b is exactly divisible by (x2 – 3x + 2) is ………………A) 0 B) 66 C) 132 D) 1

Answer»

Correct option is (A) 0

\(\because\) (x - 1) & (x - 2) are factors of \((x^3 – 6x^2 + ax + b)\)

\((\because\) (x - 1) (x - 2) \(=x^2-3x+2)\)

\(\therefore\) x = 1 and x = 2 are zeros of \((x^3 – 6x^2 + ax + b)\)

\(\therefore\) 1-6+a+b = 0 and 8-24+2a+b = 0

\(\Rightarrow\) a+b = 5 and 2a+b = 16

\(\Rightarrow\) (2a+b) - (a+b) = 16 - 5

\(\Rightarrow\) a = 11

\(\therefore\) b = 5 - a = 5 - 11 = -6

\(\therefore\) 6a+11b \(=6\times11+11\times-6\)

= 66 - 66 = 0

Correct option is A) 0