Q: Can I factor instead of using the formula?

Yes, when the roots are nice integers or simple fractions. But the quadratic formula always works, even when factoring is hard or the roots are irrational.

Q: What are Vieta's formulas?

For ax² + bx + c = 0, the sum of roots = −b/a and the product of roots = c/a. Useful for checking your answers without substituting back.

Q: How do complex roots appear?

When D < 0, the roots are x = (−b ± i√|D|) / (2a), where i = √(−1). Complex roots always come in conjugate pairs.

Q: Is every parabola described by a quadratic equation?

Yes — any quadratic equation in the form y = ax² + bx + c describes a parabola. Finding roots means finding where y = 0, i.e., where the parabola crosses the x-axis.

Question 1

What does the discriminant tell me?

Accepted Answer

D > 0: two distinct real solutions (the parabola crosses the x-axis twice). D = 0: one repeated real solution (the parabola touches the x-axis). D < 0: no real solutions (the parabola does not reach the x-axis).

Question 2

Can I factor instead of using the formula?

Accepted Answer

Yes, when the roots are nice integers or simple fractions. But the quadratic formula always works, even when factoring is hard or the roots are irrational.

Question 3

What are Vieta's formulas?

Accepted Answer

For ax² + bx + c = 0, the sum of roots = −b/a and the product of roots = c/a. Useful for checking your answers without substituting back.

Question 4

How do complex roots appear?

Accepted Answer

When D < 0, the roots are x = (−b ± i√|D|) / (2a), where i = √(−1). Complex roots always come in conjugate pairs.

Question 5

Is every parabola described by a quadratic equation?

Accepted Answer

Yes — any quadratic equation in the form y = ax² + bx + c describes a parabola. Finding roots means finding where y = 0, i.e., where the parabola crosses the x-axis.

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