JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Easy

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Application +4 | -1

\alpha ,\beta ,\gamma

are the roots of the equation

{x^3} + 4x - 1 = 0

, then

{\left( {\alpha + \beta } \right)^{ - 1}} + {\left( {\beta + \gamma } \right)^{ - 1}} + {\left( {\gamma + \alpha } \right)^{ - 1}}

is equal to

View answer and explanation

Correct option: C

- 4

Option C (-4) is correct because it is the result of simplifying the expression using Vieta's formulas for the sum and product of roots of the given cubic equation.

More Questions from THEORY OF EQUATION

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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