SOLUTION: If the roots of the quadratic equation ax*2+bx+c=0 are in the ratio of 2 : 3, then prove that 6b*2=25ac

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If the roots of the quadratic equation ax*2+bx+c=0 are in the ratio of 2 : 3, then prove that 6b*2=25ac      Log On


   

Question 1127051: If the roots of the quadratic equation ax*2+bx+c=0 are in the ratio of 2 : 3,
then prove that 6b*2=25ac
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If the roots are in the ratio 2:3, then the equation in factored form can be written as

y+=+a%28x-2n%29%28x-3n%29

Expanding....

y+=+a%28x%5E2-5nx%2B6n%5E2%29+=+ax%5E2-5anx%2B6an%5E2

Then

6b%5E2+=+6%28-5an%29%5E2+=+6%2825a%5E2n%5E2%29+=+150a%5E2n%5E2
and
25ac+=+25%28a%29%286an%5E2%29+=+150a%5E2n%5E2