Question

If one zero of the polynomial $2x^2+3x+\lambda$ is $\frac{1}{2}$, find the product of value of $\lambda$ and the other zero.

Answer 1

Sum of roots $=-\frac{3}{2}\Rightarrow \frac{1}{2}+\alpha =-\frac{3}{2}\Rightarrow \alpha =-2$

Product of roots $=\frac{\lambda }{2}\Rightarrow -2\times \frac{1}{2}=\frac{\lambda }{2}\Rightarrow \lambda =-2$

Now, $\alpha \times \lambda =-2\times -2=4$