Prove that the roots of \((b^2 - 2ac)x^2 + 4(a + c)x = 8\) are real if \(a\), \(b\), \(c\) are real. Find the conditions that the roots are equal.
Would the discriminant be helpful here?
The curve here is \(y=(b^2 - 2ac)x^2 + 4(a + c)x -8\).
What can we say about the curve if the roots of the equation are real?
What would the curve look like if the roots of the equation are equal?