SOLUTION: Find the value of c so that the quadratic equation 2x^2+4x-c=0 has two equal real roots. Can someone please help me ? I think the answer is -1/2 but I'm not sure ?!!?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the value of c so that the quadratic equation 2x^2+4x-c=0 has two equal real roots. Can someone please help me ? I think the answer is -1/2 but I'm not sure ?!!?      Log On


   

Question 121710: Find the value of c so that the quadratic equation 2x^2+4x-c=0 has two equal real roots. Can someone please help me ? I think the answer is -1/2 but I'm not sure ?!!?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B4x-c=0
To have two equal real roots, the equation has to be of the form,
f%28x%29=%28x-a%29%5E2
with 2 real roots at x=a.
If we expand that equation, we can compare terms with the original equation.
%28x-a%29%5E2=x%5E2-2a%2Ba%5E2
Let's multiply by 2.
2%28x-a%29%5E2=2x%5E2-4a%2B2a%5E2
Now let's compare.
1.x%5E2 term : 2x%5E2=2x%5E2
2.x term : -2ax=4x
3.constant term : 2a%5E2=-c
From 2,
-2ax=4x
-2a=4
a=-2
From 3,
2a%5E2=-c
c=-2a%5E2
c=-2%28-2%29%5E2
c=-2%284%29
c=-8