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Quadratic Equation and Inequalities question

2024 · 9 Apr · Shift 2 · Q37

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JEE Main
Mathematics
Quadratic Equation and Inequalities
2024 · 9 Apr · Shift 2 · Q37

Quadratic Equation and Inequalities question

2024 · 9 Apr · Shift 2 · Q37

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\alpha, \beta ; \alpha\gt \beta

, be the roots of the equation

x^2-\sqrt{2} x-\sqrt{3}=0

. Let

\mathrm{P}_n=\alpha^n-\beta^n, n \in \mathrm{N}

. Then

(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}

is equal to

A
$10 \sqrt{3} \mathrm{P}_9$
B
$11 \sqrt{3} \mathrm{P}_9$
C
$11 \sqrt{2} \mathrm{P}_9$
D
$10 \sqrt{2} \mathrm{P}_9$

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