Question

If $\alpha$ and $\beta$ are the zeros of the polynomial $f\left(x\right)=6x^2-3-7x$, then $(\alpha +1)(\beta +1)$ is equal to

• A. $\frac{5}{2}$
• B. $\frac{5}{3}$
• C. $\frac{2}{5}$
• D. $\frac{3}{5}$

Answer 1

Answer: (B)

$\frac{5}{3}$

We know that equation $a{x}^2+bx+c=0$

Then sum of roots $=\frac{-b}{a}$ and product of roots$=\frac{c}{a}$

If $\alpha$, $\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=6x^2-3-7x$, then
$(\alpha +\beta )=\frac{-b}{a}=-\frac{(-7)}{6}=\frac{7}{6},\alpha \beta =\frac{c}{a}=\frac{-3}{6}=\frac{-1}{2}$
Now, $(\alpha +1)(\beta +1)$
$=\alpha \beta +\alpha +\beta +1$
$=\frac{-1}{2}+\frac{7}{6}+1$
$=\frac{-3+7+6}{6}$
$=\frac{10}{6}$
$=\frac{5}{3}$