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Algebraic Expressions

If 2,5 are ...

Question

If $2, 5$ are zeros of polynomial find the polynomial

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Solution

Let the polynomial be $x^{2} - p x + q = 0$
$2$ is zero of polynomial so $4 - 2 p + q = 0$

$5$ is zero of polynomial so $25 - 5 p + q = 0$
So from the equations $q = 4 + 2 p q = 25 + 5 p 4 + 2 p = 25 + 5 p 21 = 3 p p = 7 q = 4 + 2 (7) q = 18$
So the polynomial is $x^{2} - 7 x + 10$

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