Start Free Mock LoginAlready registered? Login here

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediummultiple choice

The roots of the equation $x^{4} - 8 x^{3} + a x^{2} - b x + 16 = 0$ are positive, if

Options:(select one or more)

Answer:

A, D

Solution:

For positive roots $α_{1}, \dots, α_{4} : A . M . = \frac{8}{4} = 2$ and $G . M . = 1 6^{1/4} = 2. A . M . = G . M .$ , so all the roots are equal to 2. $(x - 2)^{4} = x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16$ , so $a = 24$ and $b = 32$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...