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JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

\alpha

and

\beta

be the roots of the equation

x^2+

(2 i-1)=0

. Then, the value of

\left|\alpha^8+\beta^8\right|

is equal to:

View answer and explanation

Correct option: A

50

Option A (50) is correct because, with

\alpha^2 = \beta^2 = 1 - 2i

, we find

\alpha^8 = \beta^8 = -7 + 24i

, and then

|\alpha^8 + \beta^8| = 2|-7 + 24i| = 50

.

More Questions from QUADRATIC EQUATIONS

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The solution of the equation

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

\alpha ,\beta

are the roots of

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

\alpha < 1 < \beta ,

\alpha ,\;\beta

be the roots of the equation

{x^2} - px + q = 0

{\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}}},

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

for all values of

x

a

lies in the interval If

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,

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)