Question

If the equation ax² + 2bx – 3c = 0 has no real roots and (3c/4) < a + b, then -

(A) c < 0

(B) c > 0

(C) c = 0

(D) none of

Answer 1

ax² + 2bx – 3c = 0 has no real roots

D < 0

Put x = 2 in the equation

4a + 4b – 3c = 4{(a + b) - (3c/4)} > 0

So the expression ax² + 2bx – 3c is always positive

Put x = 0 ⇒ – 3c > 0

c < 0