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23 Mar 2020
Relationship Between Solutions and Coefficients The Quadratic Formula gives us the solutions of a quadratic equation from its coefficients. We can also obtain the coefficients from the solutions.
Use the Quadratic Formula to prove that in general, if the equation
has solutions
and
, then
and ![](data:image/png;base64,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)
Relationship Between Solutions and Coefficients The Quadratic Formula gives us the solutions of a quadratic equation from its coefficients. We can also obtain the coefficients from the solutions.
Use the Quadratic Formula to prove that in general, if the equation has solutions
and
, then
and