If ${\rm{\alpha }}$ and ${\rm{\beta }}$ be two roots of the equation ${x^2} - 64x + {\rm{256 = 0}}.$ Then, the value of ${\left( {\frac{{{{\rm{\alpha }}^{\rm{3}}}}}{{{{\rm{\beta }}^{\rm{5}}}}}} \right)^{\frac{1}{8}}}{\rm{ + }}{\left( {\frac{{{{\rm{\beta }}^{\rm{3}}}}}{{{{\rm{\alpha }}^{\rm{5}}}}}} \right)^{\frac{1}{8}}}$ is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Analyzing +4 | -1

\mathrm{\alpha }

and

\mathrm{\beta }

be two roots of the equation

{x^2} - 64x + \mathrm{256 = 0}.

Then, the value of

{\left( {\frac{{{\mathrm{\alpha }^\mathrm{3}}}}{{{\mathrm{\beta }^\mathrm{5}}}}} \right)^{\frac{1}{8}}}\mathrm{ + }{\left( {\frac{{{\mathrm{\beta }^\mathrm{3}}}}{{{\mathrm{\alpha }^\mathrm{5}}}}} \right)^{\frac{1}{8}}}

View answer and explanation

Correct option: A

Option A is correct because by using Vieta's formulas and simplifying the expression, the value is equal to 2.

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