10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[(x+1)\] is a factor of \[2{{x}^{3}}+a{{x}^{2}}+2bx+1,\] then find the values of a and b given that \[2a-3b=4\]: (CBSE 2011)

A) \[a=-1,\,b=-2\]

B) \[a=2,\,b=5\]

C) \[a=5,\,b=2\]

D) \[a=2,\,b=0\]

Correct Answer: C

Solution :

[c] \[(x+1)\]is a factor of \[2{{x}^{3}}+a{{x}^{2}}+2bx+1\]

\[\therefore \,\,\,\,\,\,\,\,\,2{{(-1)}^{3}}+a{{(-1)}^{2}}-2b+1=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,a-2b=1\] (1)

Also, \[2a-3b=4\] (2)

On solving eqs. (1) and (2) we get,

\[a=5,\,b=2\]