JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Medium

1 of 1

Application +4 | -1

Let

f\left( x \right)

be a quadratic expression which is positive for all real

x

and

g\left( x \right) = f\left( x \right) + f'\left( x \right) + f''\left( x \right),

then for any real

x

View answer and explanation

Correct option: B

g\left( x \right) > 0

Option B (

g(x) > 0

) is correct because if f(x) is always positive, then g(x), which is a combination of f(x) and its derivatives, is also always positive.

More Questions from QUADRATIC EQUATIONS

Practice All Chapter MCQs →

\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)