Question

If the equation ax² − 2bx − 3c = 0 has no real roots and 4(a − b) > 3c, then c should be 

(1) negative 

(2) non-negative 

(3) positive 

(4) zero

Answer 1

Correct option (1) negative

Explanation:

f(x) ≡ ax² − 2bx − 3c = 0 has nonreal roots. 

⇒ a² f(2) f(0) > 0 

⇒ (4(a −b) − 3c)(− 3c) > 0 

⇒ c is negative 

(∴ Given 4(a − b) > 3c)