How do you show that in the quadratic function: ax^2 + bx + c with 2 roots x1 and x2 that:
1) x1 + x2 = -b/a
and
2) x1*x2 = c/a
?
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How do you show that in the quadratic function: ax^2 + bx + c with 2 roots x1 and x2 that:
1) x1 + x2 = -b/a
and
2) x1*x2 = c/a
?
Let $\displaystyle x_{1} = \frac{-b+\sqrt{b^2-4ac}}{2a}$
and $\displaystyle x_{2} = \frac{-b-\sqrt{b^2-4ac}}{2a}$
Then calculate $\displaystyle x_{1}+x_{2}= \left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)+\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)$
Alternatively:Spoiler:
Let $\displaystyle x_{1} = \frac{-b+\sqrt{b^2-4ac}}{2a}$
and $\displaystyle x_{2} = \frac{-b-\sqrt{b^2-4ac}}{2a}$
Then calculate $\displaystyle \left(x_{1}\right)\left(x_{2}\right) = \left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)$
Alternatively:
Spoiler:
$\displaystyle ax^2+bx+c = (X-X_1)(X-X_2)$
$\displaystyle X^2-(X_1 + X_2)x + X_1X_2$
then you can plug in the values for a, b and c