SOLUTION: If x and y are roots of the quadratic equation {{{ax^2+bx+c=0}}}, show that {{{x-y}}} = {{{(sqrt(b^2-4ac))/a}}} such that {{{x>y}}}. I need steps. Thanks.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If x and y are roots of the quadratic equation {{{ax^2+bx+c=0}}}, show that {{{x-y}}} = {{{(sqrt(b^2-4ac))/a}}} such that {{{x>y}}}. I need steps. Thanks.      Log On


   

Question 702261: If x and y are roots of the quadratic equation ax%5E2%2Bbx%2Bc=0, show that x-y = %28sqrt%28b%5E2-4ac%29%29%2Fa such that x%3Ey.
I need steps. Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If x and y are roots of ax%5E2%2Bbx%2Bc=0, where x > y

then by the quadratic formula

x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29

y+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29

So when you subtract y from x, you get

x-y+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29+-+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x-y+=+%28-b%2Bsqrt%28b%5E2-4ac%29+-+%28-b-sqrt%28b%5E2-4ac%29%29%29%2F%282a%29

x-y+=+%28-b%2Bsqrt%28b%5E2-4ac%29+%2B+b+%2B+sqrt%28b%5E2-4ac%29%29%2F%282a%29

x-y+=+%282%2Asqrt%28b%5E2-4ac%29%29%2F%282a%29

x-y+=+%28sqrt%28b%5E2-4ac%29%29%2Fa