Question
Question: Let f(x) = ax<sup>3</sup> + bx<sup>2</sup> + ex + d, a ≠ 0. If x<sub>1</sub> and x<sub>2</sub> are t...
Let f(x) = ax3 + bx2 + ex + d, a ≠ 0. If x1 and x2 are the real and distinct roots of f '(x) = 0 then f(x) = 0 will have three real and distinct roots if
A
x1 . x2< 0
B
f(x1) . f(x2) > 0
C
f(x1). f(x2) < 0
D
x1x2 > 0
Answer
f(x1). f(x2) < 0
Explanation
Solution
Clearly for f(x) = 0 to have three real and distinct root, signs of local maximum value and local minimum value of
y = f(x) must be opposite. Thus f(x1) . f(x2) < 0.