Write a quadratic equation with the given roots. write the equation in the form ax^2+bx+c=0 , where a, b, and c are integers. –7 and –2

  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.

step-by-step explanation:

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step-by-step explanation: