Review question

# Can we show $(b^2 - 2ac)x^2 + 4(a + c)x = 8$ always has real roots? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8812

## Suggestion

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?