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Quadratic Equation and Inequalities question

2010 · Shift 1 · Q33

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JEE Advanced
Mathematics
Quadratic Equation and Inequalities
2010 · Shift 1 · Q33

Quadratic Equation and Inequalities question

2010 · Shift 1 · Q33

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMCQ+3 / −0.75

Let

p

and

q

be real numbers such that

p e 0,\,{p^3} e q

and

{p^3} e - q.

If

{p^3} e - q.

and

\,\beta

are nonzero complex numbers satisfying

\alpha \, + \beta = - p\,

and

{\alpha ^3} + {\beta ^3} = q,

then a quadratic equation having

{\alpha \over \beta }

and

{\beta \over \alpha }

as its roots is

A
$\left( {{p^3} + q} \right){x^2} - \left( {{p^3} + 2q} \right)x + \left( {{p^3} + q} \right) = 0$
B
$\left( {{p^3} + q} \right){x^2} - \left( {{p^3} - 2q} \right)x + \left( {{p^3} + q} \right) = 0$
C
$\left( {{p^3} - q} \right){x^2} - \left( {5{p^3} - 2q} \right)x + \left( {{p^3} - q} \right) = 0$
D
$\left( {{p^3} - q} \right){x^2} - \left( {5{p^3} + 2q} \right)x + \left( {{p^3} - q} \right) = 0$

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