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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMiscellaneous/MixedMedium2 minQB

MathematicsMediumnumerical

If $2 x^{4} - 8 x^{3} + 8 x^{2} - 1 = 0$ has $n$ distinct real roots, find $1/ n$ .

Answer:

0.25

Solution:

For $F (x) = 2 x^{4} - 8 x^{3} + 8 x^{2} - 1$ , critical points are $0, 1, 2$ , with values $- 1, 1, - 1$ . Together with positive end behavior, the intermediate value theorem gives four distinct real roots. Thus $1/ n = 1/4 = 0.25$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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