Answer:
x² +9x +14 = 0
Step-by-step explanation:
Since the roots are integers, we can write the equation in the given form using a=1. Then b is the opposite of the sum of the roots:
b = -((-7) +(-2)) = 9
And c is the product of the roots:
c = (-7)(-2) = 14
So, the desired quadratic equation is ...
x² +9x +14 = 0
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The attached graph confirms the roots of this equation.
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Another way
For root r, a factor of the equation is (x -r). For the given two roots, the factors are ...
(x -(-7))(x -(-2)) = (x +7)(x +2)
When expanded, this expression is ...
x(x +2) +7(x +2) = x² +2x +7x +14
= x² +9x +14
We want the equation where this is set to zero:
x² +9x +14 = 0
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If a root is a fraction, say p/q, then the factor (x -p/q) can also be written as (qx -p). In this case, expanding the product of binomial factors will result in a value for "a" that is not 1.
