If 5 a 0 + 4 a 1 + 3 a 2 + 2 a 3 + a 4 = 0 then the equation a 0 x 4 + a 1 x 3 + a 2 x 2 + a 3 x + a 4 = 0

Start Free Mock LoginAlready registered? Login here

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumsingle choice

If $\frac{a _{0}}{5} + \frac{a _{1}}{4} + \frac{a _{2}}{3} + \frac{a _{3}}{2} + a_{4} = 0$ then the equation $a_{0} x^{4} + a_{1} x^{3} + a_{2} x^{2} + a_{3} x + a_{4} = 0$

Options:

Answer:

Solution:

Consider the function $f (x) = \frac{a _{0} x ^{5}}{5} + \frac{a _{1} x ^{4}}{4} + \frac{a _{2} x ^{3}}{3} + \frac{a _{3} x ^{2}}{2} + a_{4} x$ $f (0) = 0$ and $f (1) = 0$ by hypothesis ∴ f satisfies all conditions of Rolle's theorem $∴ f^{1} (x) = 0$ has at least one root in $(0, 1)$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Rolle's-theroem

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...