Question

If a + b + c = 0, then the equation

3ax2 + 2bx + c = 0 has, in the interval (0, 1)

• A. At least one root
• B. At most one root
• C. No root
• D. None of these

Answer 1

Answer: (A)

At least one root

Answer 2

Equation 3ax² + 2 bx + c

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

f(0) = 0

& f(1) = a + b + c = 0

⇒ f(0) = f(1) ⇒ (0, 1) are roots of f(x)

having atleast one root of f′(x)