Question

Find all values of $p$ for which the roots of the equation $(p-3)x^2-2px+5p=0$ are real and positive.

Answer 1

For real and positive root $D>0$

so , $b^2-4ac>0$

$4p^2-4\times 5p\times (p-3)$

$4p^2-20p^2+60p>0$

$-16p^2+60p$>0

$-p(16p-60)$>0

$-16p>-60$

$p<\frac{60}{16}$=$\frac{15}{4}$

Hence this the required solution