Question

The least +ve integral value of ‘a’ for which the equation

3x⁴ + 4x³ – 12x² + 5a = 0 has no real root is –

• A. 2
• B. 4
• C. 6
• D. None of these

Answer 1

Answer: (C)

6

Answer 2

Let ƒ(x) = 3x⁴ + 4x³ – 12x²

ƒ′(x) = 12x³ + 12x² – 24x

= 12x (x² + x – 2) = 0 ⇒ x = 0, 1, –2

ƒ(0) = 0, ƒ(1) = 3 + 4 – 12 = – 5

Since, ƒ(x) + 5a = 0 has no real root.

⇒ 5a > 32 ⇒ a > $\frac{32}{5}$

So, least +ve integral value of a = 6.

Hence (3) is correct answer.