(B) Let $y = x^{1/3}$. Then the equation becomes $y^2 + y - 2 = 0$.Factoring the quadratic equation: $(y + 2)(y - 1) = 0$.This gives $y = 1$ or $y = -

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(B) Let $y = x^{1/3}$. Then the equation becomes $y^2 + y - 2 = 0$.Factoring the quadratic equation: $(y + 2)(y - 1) = 0$.This gives $y = 1$ or $y = -2$.Since $y = x^{1/3}$,we have $x^{1/3} = 1 \Rightarrow x = 1^3 = 1$.And $x^{1/3} = -2 \Rightarrow x = (-2)^3 = -8$.The roots of the equation are $1$ and $-8$.The sum of the squares of the roots is $(1)^2 + (-8)^2 = 1 + 64 = 65$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The sum of squares of the roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ is

AP EAMCET 2022 All AP EAMCET

A
$82$
B
$65$
C
$50$
D
$37$

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Solution of quadratic equations and Nature of roots

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