Application of DerivativeHard
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
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
If length of subnormal at any point of the curve yn = an-1x is constant, then n equals-If length of subnormal at any poi...The length of normal to the curve = a(t + sin t), y = a(1−cos t) at any point t is -...A particle begins at the origin and moves successively in the following manner as shown, 1unit to the right, 1/2 unit up...The equation of the normal to the curve x = a cos3 t, y = a sin3 t at ′t′ point is-...If tangent to a curve at a point is perpendicular to x-axis, then at that point-...