If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x)=k x^{2} -30 x+45 k$ and $\alpha+\beta=\al

Question

If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x)=k x^{2} -30 x+45 k$ and $\alpha+\beta=\alpha \beta$, then the value of ' $k$ ' is:\

Professor PC Thomas Classes · Answer

(d) : Given, $\alpha$ and $\beta$ are zeroes of the polynomial
 $p(x)=k x^{2}-30 x+45 k$\ Here, $a=k, b=-30, c=45 k$\ Sum of zeroes $=\alpha+\beta=\frac{-b}{a}=\frac{30}{k}$\ Product of zeroes $=\alpha \beta=\frac{c}{a}=\frac{45 k}{k}=45$\ $\because \quad \alpha+\beta=\alpha \beta$\ [Given]\ $\Rightarrow \frac{30}{k}=45 \Rightarrow k=\frac{30}{45}=\frac{2}{3}$