Application of DerivativeHard
Question
If 2a + 3b + 6c = 0, then at least one root of the equation ax2 + bx + c = 0 lies in the interval-
Options
A.(0, 1)
B.(1, 2)
C.(2, 3)
D.none
Solution
2a + 3b + 6c = 0
ax2 + bx + c = 0 has at least one roots
It proves Rolle′s theorem
∫f′(x)dx = ∫(ax2 + bx + c)dx
f(x) =
+ d
so f(x) =
+ d
for Rolle′s theorem
f(a) = f(b), (a, b) is interval given
So given (0, 1)
f(0) = d
f(1) =
+ d
f(1) = d
so f(0) = f(1) so the (0, 1) correct
ax2 + bx + c = 0 has at least one roots
It proves Rolle′s theorem
∫f′(x)dx = ∫(ax2 + bx + c)dx
f(x) =
+ dso f(x) =
+ dfor Rolle′s theorem
f(a) = f(b), (a, b) is interval given
So given (0, 1)
f(0) = d
f(1) =
+ df(1) = d
so f(0) = f(1) so the (0, 1) correct
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