Find the values of “a” and “b” so that (x + 2) and (x – 1) may be factors of x^3 + 10x^2 + ax + b.
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
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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
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