JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

The values of '

a

' for which

\left( {{a^2} - 1} \right){x^2} + 2\left( {a - 1} \right)x + 2

is positive for any

x

, are

View answer and explanation

Correct option: D

a < - 3\,\,\mathrm{or}\,\,a > 1

Option D (

a < - 3\,\,\mathrm{or}\,\,a > 1

) is correct because the expression is positive for all

x

a^2 - 1 > 0

and the discriminant is negative, leading to the solution

a < -3

a > 1

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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\;

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

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