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Write a polynomial equation with integer coefficients that has the given roots. x=-2 x=3

User Rretzbach
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Answer:


\boxed{x^2 - x - 6}

Explanation:

If a is the root of a polynomial then x-a is a factor of that polynomial

Since - 2 is a root, x -(-2) = x + 2 is a factor

Since 3 is a root, x - 3 is a factor

Multiplying the factors of a polynomial gives you the polynomial equation

So the polynomial equation is


(x + 2)(x-3)

Apply FOIL method:

(x + 2)(x-3) \\\\= x\cdot x+ x\left(-3\right)+2x+2\left(-3\right)\\\\= x^2 -3x + 2x -6\\\\x^2 - x - 6\\\\Answer: \boxed{x^2 - x - 6}

User Johnnycakes
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