Question

If $\alpha$ and $\beta$ are the zeros of polynomial $p\left(x\right)=x^2-3x+3k$ and $\alpha +\beta =\alpha .\beta$ then $k$=

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

Answer 1

The correct option is A $1$

The quadratic equation is $x^2-3x+3k=0$

Sum of roots $\alpha +\beta =\frac{-b}{a}=3$

Product of roots $\alpha .\beta =\frac{c}{a}=3k$

The given condition is $\alpha +\beta =\alpha .\beta$

$⟹3=3k$

$⟹k=1$