Definite IntegrationHard
Question
If a, b, c ∈ R and satisfy 3a + 5b + 15c = 0, the equation ax4 + bx2 + c = 0 has -
Options
A.at least one root in (-1, 0)
B.at least one root in (0, 1)
C.at least two roots in (-1 , 1)
D.no root in (-1, 1)
Solution
Let f(x) = 
+ cx
It is continuous & differentiable everywhere
Now f(0) = 0, f(1) =
= 0
and f(-1) = 0
so f′(x) = 0 will have at least one root in (-1, 0) atleast one root in (0, 1) so it will have atleast two roots in (-1, 1)
+ cxIt is continuous & differentiable everywhere
Now f(0) = 0, f(1) =
= 0and f(-1) = 0
so f′(x) = 0 will have at least one root in (-1, 0) atleast one root in (0, 1) so it will have atleast two roots in (-1, 1)
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