Let $\alpha $ and $\beta $ be the roots of the equation, $5{x^2} + 6x - 2 = 0.$ If ${S_n} = {\alpha ^n} + {\beta ^n},$ $n = 1,2,3.....$ then

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Application +4 | -1

Let

\alpha

and

\beta

be the roots of the equation,

5{x^2} + 6x - 2 = 0.

{S_n} = {\alpha ^n} + {\beta ^n},

n = 1,2,3.....

then

View answer and explanation

Correct option: D

5{S_6} + 6{S_5} = 2{S_4}

The correct answer is D (

5{S_6} + 6{S_5} = 2{S_4}

) because it directly applies Newton's Theorem for recurrence relations of roots of a polynomial equation.

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