Application of DerivativeMedium
Question
If a + b + c = 0, then the equation 3ax2 + 2bx + c = 0 has, in the interval (0, 1) -
Options
A.Atleast one root
B.Atmost one root
C.No root
D.none of these
Solution
a + b + c = 0
f′(x) = 3ax2 + 2bx + c
f(x) = ax3 + bx2 + cx + d
f(0) = d
f(1) = (a + b + c + d)
f(1) = 0 + d
f(0) = d
f(0) = f(1)
Rolle′s proved
So it have at least one root
f′(x) = 3ax2 + 2bx + c
f(x) = ax3 + bx2 + cx + d
f(0) = d
f(1) = (a + b + c + d)
f(1) = 0 + d
f(0) = d
f(0) = f(1)
Rolle′s proved
So it have at least one root
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