Vieta's Formula

Algebra Level pending

Find the area of a triangle whose base is greater than the height, with them being the real solutions of x 2 − 12345 x + 67890 x^2-12345x+67890 .


The answer is 33945.

Christopher Ho by Christopher Ho , 17, USA

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2 solutions

Christopher Ho
Mar 22, 2017

Using vieta's, we know the product of the roots (The base times the height) is equal to 67890. The area of a triangle can be given by

base * height / 2,

so we simply compute 67890/2 = 33945

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The product base*height is the double of the note term thus let's divide it by 2.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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