10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[\alpha \] and \[\beta \] are the zeroes of the polynomial \[2{{y}^{2}}+7y+5\], then the value of \[\alpha +\beta +\alpha \beta \]is

A) -1

B) 0

C) 1

D) 2

Correct Answer: A

Solution :

\[\alpha\] and \[\beta\]are the zeroes of \[2{{y}^{2}}+7y+5\]

We know that, \[\alpha +\beta =-\frac{b}{a}=-\frac{7}{2}\]

\[\alpha \,.\,\beta =\frac{c}{a}=\frac{5}{2}\]

\[\Rightarrow \,\left( \alpha +\beta \right)+\left( \alpha \,.\,\beta \right)=-\frac{7}{2}+\frac{5}{2}=\frac{-7+5}{2}=-1\]