JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Application +4 | -1

The quadratic equation whose roots are the squares of the sum and difference of the roots of

a x^2+b x+c

=0

View answer and explanation

Correct option: C

a^4 x^2-2 a^2\left(b^2-2 c a\right) x+b^2\left(b^2-4 c a\right)=0

Option C (

a^4 x^2-2 a^2(b^2-2 c a) x+b^2(b^2-4 c a)=0

) is correct because it is derived by finding the sum and product of the squares of the sum and difference of the roots of the given quadratic equation.

More Questions from QUADRATIC EQUATIONS

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The solution of the equation

\log _7 \log _5(\sqrt{x+5}+\sqrt{x})=0

is If

\alpha ,\beta

are the roots of

{x^2} - 3x + a = 0,a \in R

and

\alpha < 1 < \beta ,

then If

\alpha ,\;\beta

be the roots of the equation

{x^2} - px + q = 0

and

{\alpha _1},{\beta _1}

be the roots of the equation

{x^2} - qx + p = 0,

then the equation whose roots are

\frac{1}{{{\alpha _1}\beta }} + \frac{1}{{\alpha {\beta _1}}}\mathrm{and}\;\frac{1}{{\alpha {\alpha _1}}} + \frac{1}{{\beta {\beta _1}}},

is If

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

for all values of

x

, then

a

lies in the interval If

f\left( x \right) = a{x^2} + bx + c\;

and

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

and

\;a \ne 0,

then Root(s) of the equation

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

belonging to the domain of definition of the function

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)

is (are)