Question

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

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

Answer 1

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

$\begin{array}{c}{x}^2-3x+2k\\ \alpha +\beta =+3\\ \alpha \beta =2k\\ \alpha +\beta =\alpha \beta \\ \Rightarrow +3=2k\\ \Rightarrow k=\frac{3}{2}\end{array}$