Let $\alpha $ and $\beta $ be the roots of equation $p{x^2} + qx + r = 0,\,\,\,p \ne 0.$ If $p,\,\,q$ and $r$ are in AP and $\frac{1}{\alpha } + \frac{1}{\beta } = 4,$ then the value of $\left| {\alpha - \beta } \right|$ is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Let

\alpha

and

\beta

be the roots of equation

p{x^2} + qx + r = 0,\,\,\,p \ne 0.

p,\,\,q

and

r

are in AP and

\frac{1}{\alpha } + \frac{1}{\beta } = 4,

then the value of

\left| {\alpha - \beta } \right|

View answer and explanation

Correct option: D

\frac{{2\sqrt {13} }}{9}

Option D (

\frac{{2\sqrt {13} }}{9}

) is correct because by using the given conditions and properties of arithmetic progressions and quadratic equations, the value of

\left| {\alpha - \beta } \right|

is calculated to be

\frac{{2\sqrt {13} }}{9}

Practice All Chapter MCQs →

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x

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