JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Analyzing +4 | -1

Let

\alpha ,\beta

be the roots of the equation

{x^2} - px + r = 0

and

\frac{\alpha }{2},\;2\beta

be the roots of the equation

{x^2} - qx + r = 0

. Then the value of

r

View answer and explanation

Correct option: D

\frac{2}{9}\left( {2p - q} \right)\left( {2q - p} \right)

Option D (

\frac{2}{9}(2p - q)(2q - p)

) is correct because solving the system of equations derived from Vieta's formulas yields this expression for r.

More Questions from QUADRATIC EQUATIONS

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\log _7 \log _5(\sqrt{x+5}+\sqrt{x})=0

\alpha ,\beta

{x^2} - 3x + a = 0,a \in R

\alpha < 1 < \beta ,

\alpha ,\;\beta

{x^2} - px + q = 0

{\alpha _1},{\beta _1}

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

\frac{1}{{{\alpha _1}\beta }} + \frac{1}{{\alpha {\beta _1}}}\mathrm{and}\;\frac{1}{{\alpha {\alpha _1}}} + \frac{1}{{\beta {\beta _1}}},

{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)