Question
Question: The equation 3x<sup>2</sup> + 4ax + b = 0 has at least one root in (0,1) if...
The equation 3x2 + 4ax + b = 0 has at least one root in (0,1) if
A
4a + b + 3 = 0
B
2a + b + 1 = 0
C
b = 0, a = – 4/3
D
None
Answer
2a + b + 1 = 0
Explanation
Solution
Let f '(x) = 3x2 + 4ax + b
\ f(x) = x3 + 2ax2 + bx + c
Q it is polynomial \ it is continuous & differentiable & f '(x) = 0 has at least one root in (0, 1)
\ it follow Rolle's theorem in [0, 1]
\ f(0) = f(1) Ž c = 1 + 2a + b + c
Ž 2a + b + 1 = 0