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  4. If p, q are odd integers, then the roots of the equation 2px2 + (2p + q)x + q = 0 are

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Q. If $p, q$ are odd integers, then the roots of the equation $2px^2 + (2p + q)x + q = 0$ are

WBJEEWBJEE 2017Complex Numbers and Quadratic Equations

Solution:

Given equation,
$2 p x^{2}+(2 p+q) x+q=0$
$\therefore D =(2 p+q)^{2}-4(2 p)(q)$
$=4 p^{2}+q^{2}+4 p q-8 p q$
$=4 p^{2}+q^{2}-4 p q $
$=(2 p-q)^{2}$
$=$ a perfect square
$\therefore $ Given equation has rational roots