Find a quadratic polynomial whose zeros are $3$ and $2$ .

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Solution

Roots are $3, 2$
Equation is $(x - 3) (x - 2) = 0$
$x^{2} - 3 x - 2 x + 6 = 0$
$x^{2} - 5 x + 6 = 0$
So polynomials is $p (x) = x^{2} - 5 x + 6$

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