Question

if $p,q$ are roots of $4x^2-(5a+1)x+5a=0$ and $q=1+p$. Find the values of $a,p$ and $q$.

Answer 1

$4x^2-(5a+1)x+5a=0$ has roots p, q

Also $q=1+p$

$\therefore p+q=\frac{5a+1}{4}$

$\therefore pq=\frac{5a}{4}$

$\therefore p+1+p=\frac{5a+1}{4}$

$\therefore 2p+1=\frac{5a+1}{4}$ ………$\left(1\right)$

$\therefore p(1+p)=\frac{5a}{4}$ ………..$\left(2\right)$

$\therefore$ From $\left(1\right)$ & $\left(2\right)$, we have $p=\frac{3}{2}$ $a=3^{\prime }$

$\therefore q=\frac{5}{2}$

Answer: $\therefore$ Value of $p=\frac{3}{2}$

$a=3$

& $q=\frac{5}{2}$.