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

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) (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.

RELATED QUESTIONS
if the sum of the roots of quadratic equation, ax^2+bx+c=0, is equal to the sum of cubes... (answered by Edwin McCravy,AnlytcPhil)

prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then... (answered by math_tutor2020)

prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then... (answered by ikleyn)

what is the sum of the roots of the equation ax exponent 2+bx+c=0? (answered by Earlsdon)

What is the sum of the roots of the equation... (answered by jim_thompson5910,stanbon)

What is the sum of the roots of the equation ax^2 + bx + c... (answered by htmentor)

What is the sum of the roots of the equation ax(squared) +bx +c... (answered by Alan3354)

If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and... (answered by ikleyn,MathTherapy)

If α(alpha) and β (beta) are the roots of the equation ax^2+bx+c,then the value (answered by reviewermath)