Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsEasy2 minPYQ_2021

MathematicsEasysingle choice

Let $α, β$ be two roots of the equation $x^{2} + {(20)}^{1 / 4} x + {(5)}^{1 / 2} = 0$ . Then $α^{8} + β^{8}$ is equal to

Answer:

Solution:

Given,

$x^{2} + {(20)}^{1 / 4} x + {(5)}^{1 / 2} = 0$

$\Rightarrow x^{2} + (\sqrt{5}) = - x {(20)}^{\frac{1}{4}}$

$\Rightarrow {(x^{2} + \sqrt{5})}^{2} = \sqrt{20} x^{2}$

$\Rightarrow x^{4} + 5 + 2 \times x^{2} \times \sqrt{5} = \sqrt{20} x^{2}$

$\Rightarrow x^{4} = - 5 \Rightarrow x^{8} = 25$

So, $α^{8} + β^{8} = 25 + 25 = 50$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2021

Loading discussions...