Answer:
c=-35/4
Explanation:
For this, we would use Vieta's theorem, which states the roots of the equation added together would equal -b/a, x₁ + x₂ = -b/a
Lets create a system with this:
x₁ - x₂ = 6 (This is given from the problem)
x₁ + x₂ = -b/a or -1/1, plugging in the values from your equation
next, we would add these systems together
x₁ + x₂ + (x₁ - x₂) = 6 + (-1)
x₁ + x₁ = 5
2x₁ = 5
x₁ = 2.5
If we plug x₁ back in, we get:
2.5 - x₂ = 6
-x₂ = 3.5
x₂ = -3.5
Now that we have the roots, we can use Vieta's theorem again to say
x₁ * x₂ = c/a
Plugging this in, we get:
2.5 * -3.5 = c/a
Lets change things to fractions to make things easier
5/2 * -7/2 = c/a
Plugging in a, we get
-35/4 = c/1
-35 = 4c
c = -35/4
Hope this helps!