Find the value of a and b so that the polynomial x3 – 4x2 + ax + b is exactly divisible by x – 2 as well as x + 1.
+118609 Find the value of a and b so that the polynomial x3 – 4x2 + ax + b is exactly divisible by x – 2 as well as x + 1.
\(f(x)=x^3-4x^2+ax+b\\ f(2)=8-16+2a+b=0\\ \qquad 2a+b=8 \qquad(1)\\ f(-1)=-1-4-a+b=0\\ \qquad -a+b=5 \qquad(2) \)
Now solve equations 1 and 2 simultaneously.
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