Question

The values of 'a' for which the roots of the equation

x² + x + a = 0 are real and exceed 'a' are –

• A. 0 < a <¼
• B. a < 1/4
• C. a < – 2
• D. – 2 < a < 0

Answer 1

Answer: (C)

a < – 2

Answer 2

(i) D = b² – 4ac ³ 0 (ii) af(k) > 0 ; (iii) $\frac{- b}{2a}$ > k

1–4a > 0 ; f(1) > 0 ; $\frac{- 1}{2}$ >a

a < $\frac{1}{4}$ ; a² + 2a > 0 ; a < $\frac{- 1}{2}$

a < $\frac{- 1}{2}$ & a² + 2a > 0

a < $\frac{- 1}{2}$ & a (a + 2) > 0

a < $\frac{- 1}{2}$ & a + 2 < 0 {Q a < 0}

a < $\frac{- 1}{2}$ & a < – 2 Ž a < – 2