JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

\alpha ,\;\beta ,\;\gamma

are the roots of the equation

{x^3} - 7x + 7 = 0

, then

\frac{1}{{{\alpha ^4}}} + \frac{1}{{{\beta ^4}}} + \frac{1}{{{\gamma ^4}}}

View answer and explanation

Correct option: B

\frac{3}{7}

Option B (

\frac{3}{7}

) is correct because it involves using Vieta's formulas and algebraic manipulation to find the sum of the reciprocals of the fourth powers of the roots.

More Questions from THEORY OF EQUATION

Practice All Chapter MCQs →

The maximum number of real roots of the equation

{x^{2n}} - 1 = 0

is The number of roots of the equation

\frac{1}{x}+\frac{1}{\sqrt{\left(1-x^2\right)}}=\frac{35}{12}

is How many real solutions does the equation

x^7+14 x^5+16 x^3+30 x-560=0

have? If

x_1, x_2, x_3, \ldots, x_n

are the roots of the equation

x^n+a x+b=0

, the value of

\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_1-x_4\right) \ldots\left(x_1-x_n\right)

is The polynomials

P(x)=k x^3+3 x^2-3

and

Q(x)=2 x^3-5 x+k

, when divided by

(x-4)

leave the same remainder, then

k

is equal to: If

{\left( {x - 1} \right)^3}

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

then the other factor is