Question

1- Find the value of p for which the product of roots of the quadratic equation px^2+6x+4p = 0 is equal to the sum of the roots.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given equation:

$\sf{p {x}^{2} + 6x + 4p = 0}$

Comparing with the formula of quadratic equation,

$\sf{a {x}^{2} + bx + c = 0 }$

Here,

$\sf{Sum \: of \: roots( \alpha ) = \frac{ - b}{a} = - 6}$

$\sf{Product \: of \: roots ( \beta ) = \frac{c}{a} = 4p }$

Thus,

$\sf{ \frac{ - b}{a} = \frac{c}{a} }$

$\sf{\implies \: - 6 = 4p}$

$\sf{\implies \: p = \frac{ - 6}{4} = \frac{ - 3}{2} }$

Hence, p = -3/2 or 1.5