Question

If 27a + 9b + 3c + d = 0, then the equation

4ax3 + 3bx2 + 2cx + d = 0, has at least one real root lying between

• A. 0 and 1
• B. 1 and 3
• C. 0 and 3
• D. None of these

Answer 1

Answer: (C)

0 and 3

Answer 2

$\frac{4ax^{4}}{4}$ + $\frac{3bx^{3}}{3}$ + $\frac{2cx^{2}}{2}$ + dx = f(x)

f(x) = ax⁴ + bx³ + cx² + dx

By option x = 0 → f(0) = 0

x = 1 → f(1) = a + b + c + d ≠ 0

x = 3 → f(3) = 27 a + 9b + 3c + d = 0

⇒ x = (0, 3) has atleast one root of equation