JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Analyzing +4 | -1

\alpha

and

\beta

are the solutions of the quadratic equation

a{x^2} + bx + c = 0

such that

\beta = {\alpha ^{1/3}}

, then

View answer and explanation

Correct option: C

{\left( {{a^3}c} \right)^{1/4}} + {\left( {a{c^3}} \right)^{1/4}} + b = 0

Option C (

{\left( {{a^3}c} \right)^{1/4}} + {\left( {a{c^3}} \right)^{1/4}} + b = 0

) is correct because it is derived from the given condition

\beta = {\alpha ^{1/3}}

and the relationships between the roots and coefficients of the quadratic equation.

More Questions from QUADRATIC EQUATIONS

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\alpha ,\beta

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\alpha ,\;\beta

{x^2} - px + q = 0

{\alpha _1},{\beta _1}

{x^2} - qx + p = 0,

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{x^2} + 4ax + 2 > 0

x

a

f\left( x \right) = a{x^2} + bx + c\;

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

\;a \ne 0,

9{x^2} - 18\left| x \right| + 5 = 0

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)