SOLUTION: If the sum of the roots of equation ax^2+4x+c=0 is half of their difference.then find the value of ac

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Question 1053874: If the sum of the roots of equation ax^2+4x+c=0 is half of their difference.then find the value of ac
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic formula
x=(1/2a)(-4+/-sqrt(16-4ac)
Add the roots
(1/2a))[-4+sqrt(16-4ac)-4-sqrt(16-4ac)]=(1/2a)(-8)=-4/a
Subtract the roots
(1/2a)[-2sqrt(16-4ac)]=-sqrt(16-4ac)/a
Half the difference is -sqrt(16-4ac)/2a
That equals the sum, -4/a or -8/2a
They equal each other
-8=-sqrt(16-4ac)
multiply by -1 and square both sides
64=16-4ac
48=-4ac
ac=-12
If a is 1, then c is -12
The equation is x^2+4x-12=0
that factors into (x+6) and (x-2)
roots -6 and 2 sum to -4.
The difference is -8, so the sum is half the difference.