Question

If the quadratic equation ax² + bx + 6 = 0 does not have real roots and b∈ R⁺, then-

• A. a > max. $\left\{ \frac{b^{2}}{24},b - 6 \right\}$
• B. a< max. $\left\{ \frac{b^{2}}{24},b - 6 \right\}$
• C. a> min. $\left\{ \frac{b^{2}}{24},b - 6 \right\}$
• D. a < min. $\left\{ \frac{b^{2}}{24},b - 6 \right\}$

Answer 1

Answer: (A)

a > max. $\left\{ \frac{b^{2}}{24},b - 6 \right\}$

Answer 2

ax² + bx + 6 = 0, roots are not real

⇒ D < 0 ⇒ b² – 24a < 0 ⇒ a > $\frac{b^{2}}{24}$ i.e., a is +ve …(1)

Also ƒ(–1) > 0 ⇒ a – b + 6 > 0

⇒ a > b – 6 …(2)

⇒ a > max. $\left\{ \frac{b^{2}}{24},b\ –6 \right\}$; using (1) and (2)

Hence (1) is correct answer.