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

Question

If p, q are odd integers, then the roots of the equation 2px2 + (2p + q)x + q = 0 are (A) rational (B) irrational (C) non-real (D) equal

Tardigrade Admin · Accepted Answer

Given equation, 2 p x2+(2 p+q) x+q=0 ∴ D =(2 p+q)2-4(2 p)(q) =4 p2+q2+4 p q-8 p q =4 p2+q2-4 p q =(2 p-q)2 = a perfect square ∴ Given equation has rational roots

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

rational

irrational

non-real

equal

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

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