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373. If one root of the polynomial p(x) = 5x² + 13x + K is reciprocal of the other. Find the value of K.

We have,
$space space space straight p left parenthesis straight x right parenthesis space equals space 5 straight x squared plus 13 straight x plus straight K$
Let first root be $space straight alpha comma$ then other root $equals space 1 over straight alpha$
Now, products of the roots = $fraction numerator Consant space term over denominator Coeff. space of space straight x squared end fraction$
$rightwards double arrow$ $straight alpha.1 over straight alpha equals straight K over 5$

$rightwards double arrow$ $1 equals straight K over 5$

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Hence, K = 5