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If I have a linear function and some kind of quadratic in x and y ie: $x^2+xy+y^2=1$ that share two roots, then I can substitute that linear function into the quadratic expression and use the Sum of Roots formulae to find the midpoint of the chord.

My question is: Is there a similar geometric application of the Product of Roots?

Trogdor
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1 Answers1

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If you want to find the difference between the two intersections, then you may want to use the formula

$$ |x_1 - x_2| = \sqrt{(x_1 + x_2)^2 - 4x_1x_2}$$

Empiricist
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