The roots of $x^{2} - 10 x + 21 = 0$ are p and q. Find $p^{3} + q^{3}$

539

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152

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243

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370

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Solution

The correct option is B 370
$x^{2} - 10 x + 21 = 0$
$=> x^{2} - 7 x - 3 x + 7 \times 3 = 0$
$=> x (x - 7) - 3 (x - 7) = 0$
$=> x = 7, 3$
Let $p = 7, q = 3$
And $p^{3} + q^{3} = 7^{3} + 3^{3} = 343 + 27 = 370$

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