Find the values of “a” and “b” so that (x + 2) and (x – 1) m

1.	Find the values of “a” and “b” so that (x + 2) and (x – 1) may be factors of x3 + 10x2 + ax + b. A) a = 7,b = -18 B) a = 7, b = -17 C) a = 7, b = -15 D) a = 7, b = 17
Answer» Correct option is (A) a = 7, b = -18 \(\because\) (x + 2) and (x – 1) are factors of \(x^3 + 10x^2 + ax + b.\) \(\Rightarrow\) x = -2 and x = 1 are zeros of \(x^3 + 10x^2 + ax + b.\) \(\therefore\) \((-2)^3+10.(-2)^2+a\times-2+b=0\) and 1+10+a+b = 0 \(\Rightarrow\) -8+40-2a+b = 0 and b = -a - 11 \(\Rightarrow\) 32 - 2a - a - 11 = 0 \(\Rightarrow\) 3a = 32 - 11 = 21 \(\Rightarrow\) a = \(\frac{21}3\) = 7 \(\therefore\) b = -a - 11 = -7 - 11 = -18 Correct option is A) a = 7,b = -18

Find the values of “a” and “b” so that (x + 2) and (x – 1) may be factors of x3 + 10x2 + ax + b. A) a = 7,b = -18 B) a = 7, b = -17 C) a = 7, b = -15 D) a = 7, b = 17

Answer»

Correct option is (A) a = 7, b = -18

\(\because\) (x + 2) and (x – 1) are factors of \(x^3 + 10x^2 + ax + b.\)

\(\Rightarrow\) x = -2 and x = 1 are zeros of \(x^3 + 10x^2 + ax + b.\)

\(\therefore\) \((-2)^3+10.(-2)^2+a\times-2+b=0\) and 1+10+a+b = 0

\(\Rightarrow\) -8+40-2a+b = 0 and b = -a - 11

\(\Rightarrow\) 32 - 2a - a - 11 = 0

\(\Rightarrow\) 3a = 32 - 11 = 21

\(\Rightarrow\) a = \(\frac{21}3\) = 7

\(\therefore\) b = -a - 11 = -7 - 11 = -18

Correct option is A) a = 7,b = -18