Question

Find the quadratic polynomial whose one zero is 5 and the product of roots is 30.

Answer 1

One zero say $\alpha =5$

Product of roots$=30$

Another root be $=\beta$

We know, $\alpha \cdot \beta =30$

$\Rightarrow \beta =\frac{30}{5}$

$\Rightarrow \beta =6$

Polynomial :$(x-\alpha )(x-\beta )=0$

$\Rightarrow p\left(x\right):(x-6)(x-5)=0$

$\Rightarrow p\left(x\right):x^2-11x+30$