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Relationship between Zeroes and Coefficients of a Polynomial

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Question

Check following are quadratic
$3 x (4 + 5 x) + (3 + 4 x) 4 x$

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Solution

$3 x (4 + 5 x) + (3 + 4 x) 4 x$
$= 12 x + 15 x^{2} + 12 x + 16 x^{2}$
$= 24 x + 41 x^{2}$
As highest degree in the polynomial is 2
so it is quadratic

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