Question

If $\alpha ,\beta$ are the zeroes of $f\left(x\right)=p{x}^2-2x+3p$ and $\alpha +\beta =\alpha \beta ,$ then the value of $p$ is :

• A. $\frac{1}{3}$
• B. $-\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $-\frac{2}{3}$

Answer 1

The correct option is C $\frac{2}{3}$

Given: $\alpha ,\beta$ are zeroes of the polynomial $f\left(x\right)=p{x}^2-2x+3p$, and $\alpha +\beta =\alpha \beta$

To find the value of p

Sol: From the given quadratic equation,

$\alpha +\beta =\frac{2}{p}$ and $\alpha \beta =3$

but it is given,

$\alpha +\beta =\alpha \beta ⟹\frac{2}{p}=3⟹p=\frac{2}{3}$