JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Hard

1 of 1

Analyzing +4 | -1

Let

a,b,c

be real number

a \ne 0.\,\mathrm{If}\;\alpha

is a root of

{a^2}{x^2} + bx + c = 0,\;\beta

is a root of

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

and

0 < \alpha < \beta

, then the equation

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

has a root of

\gamma

that always satisfies

View answer and explanation

Correct option: D

\alpha < \gamma < \beta

Option D (

\alpha < \gamma < \beta

) is correct because by Intermediate Value Theorem, since f(α) and f(β) have opposite signs, there must be a root between α and β.

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