Question

$\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=k{x}^2+2x+3k$. Find the value of $k$, if $\alpha +\beta =\alpha \beta$.

Answer 1

$\alpha +\beta =\alpha \beta$

$\therefore \alpha +\beta =-\frac{b}{a}$

$\therefore \alpha \beta =\frac{c}{a}$

$\therefore \frac{-b}{a}=\frac{c}{a}$

$\therefore -b=c$

$\therefore -2=3k$

$\therefore k=\frac{-2}{3}$