If $f\left( x \right) = {x^2} + 2bx + 2{c^2}\;{\rm{and\;g}}\left( x \right) = - {x^2} - 2cx + {b^2}\;{\rm{such\;that}}\min f\left( x \right) > \max {\rm{g}}\left( x \right),$ then the relation between $b$ and $c$ is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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f\left( x \right) = {x^2} + 2bx + 2{c^2}\;\mathrm{and\;g}\left( x \right) = - {x^2} - 2cx + {b^2}\;\mathrm{such\;that}\min f\left( x \right) > \max \mathrm{g}\left( x \right),

then the relation between

b

and

c

View answer and explanation

Correct option: D

\left| c \right| > \left| b \right|\sqrt 2

Option D (

\left| c \right| > \left| b \right|\sqrt 2

) is correct because the condition

\min f(x) > \max g(x)

leads to the inequality

\left| c \right| > \left| b \right|\sqrt 2

Practice All Chapter MCQs →

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{\alpha _1},{\beta _1}

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

x

a

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