Question

1. If $\alpha$ and $\beta$ are the zeroes of the polynomial $2y^2+7y+5,$ write the values of $\alpha +\beta +\alpha \beta .$.

2. For what value of ${}^{\prime }{k}^{\prime },k-3,2k+1$ and $4k+3$ are in A.P.

Answer 1

1) $2y^2+7y+5=(2y+5)(y+1)$

Sum of the roots of given equation =$\alpha +\beta =\frac{-7}{2}$

Product of the roots of given equation $\alpha \beta =\frac{5}{2}$

$\alpha +\beta +\alpha \beta =\frac{-7}{2}+\frac{5}{2}=-1$

2)For three numbers to be in AP $2b=a+c$

Therefore $c=4k+3,a=k-3,b=2k+1$

$2(2k+1)=k-3+4k+3$

$4k+2=5k$

$k=2$