Question

find the value of p for which the equation p x square minus five x plus b equals to zero has equal roots

Answer 1

Dear Student,

$$\begin{gathered} p\left(x\right)=p{x}^2-5x+b \\ Itisgiventhatp\left(x\right)hasequalroots,i.e.thediscriminantwillbezero. \\ Discriminant\left(D\right)=0,b^2-4ac=0 \\ {\left(-5\right)}^2-4\times p\times b=0 \\ 25-4pb=0 \\ 4pb=25 \\ \mathit{p}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{25}}{\mathbf{4}\mathbf{b}} \end{gathered}$$
Regards