JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Let

f(x)

be a quadratic expression such that

f(x) <

0 \forall x \in \boldsymbol{R}

. If

g(x)=f(x)+f^{\prime}(x)+f^{\prime \prime}(x)

then for

x \in \boldsymbol{R}

View answer and explanation

Correct option: A

g(x) < 0

Option A (

g(x) < 0

) is correct because if

f(x)

is a quadratic expression always less than 0, then

g(x) = f(x) + f'(x) + f''(x)

is also always less than 0.

More Questions from QUADRATIC EQUATIONS

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\alpha ,\beta

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\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

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