Question

Solve
Q.2. If (x - 3) and (x - $\frac{1}{3}$) are both factors of $\left(p{x}^2+5x+r\right)$ then show that p = r.

Answer 1

Dear Student,

$$\begin{gathered} \left(x-3\right)and\left(x-\frac{1}{3}\right)arefactorsofp{x}^2+5x+r \\ \therefore rootsarex=3andx=\frac{1}{3} \\ asweknowproductofrootsofequation=\frac{cons\tan tterm}{coefficientof{x}^2} \\ \Rightarrow 3\times \frac{1}{3}=\frac{r}{p} \\ \Rightarrow \frac{r}{p}=1 \\ \Rightarrow r=p \\ Henceproved \end{gathered}$$

Regards,