Quiz: The Quadratic Formula

🧠 Quiz: The Quadratic Formula

1. What is the general form of a quadratic equation?

\( ax^2 + bx + c = 0 \) \( ax + b = 0 \) \( ax^3 + bx^2 + c = 0 \) \( ax^2 + c = 0 \)

2. What is the quadratic formula?

\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) \( x = \frac{-a \pm \sqrt{b^2 - 4ac}}{2b} \) \( x = \frac{-b \pm \sqrt{4ac - b^2}}{2a} \) \( x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a} \)

3. What is the discriminant in the quadratic formula?

\( b^2 - 4ac \) \( b^2 + 4ac \) \( 2a + b \) \( a^2 - b^2 \)

4. If the discriminant is negative, the roots are:

Real and equal Real and distinct Complex Irrational

5. Solve \( x^2 - 4x + 3 = 0 \) using the quadratic formula.

\( x = 1, x = 3 \) \( x = -1, x = -3 \) \( x = 2 \pm \sqrt{1} \) \( x = 2 \pm \sqrt{3} \)

6. Solve \( x^2 + 2x + 5 = 0 \) using the quadratic formula.

\( x = -1 \pm \sqrt{5} \) \( x = -1 \pm \sqrt{-4} \) \( x = -1 \pm 2i \) \( x = -2 \pm \sqrt{1} \)

7. What type of roots does the equation \( x^2 + 4x + 4 = 0 \) have?

Two distinct real roots Two complex roots One real root (repeated) Two irrational roots

8. Solve \( 2x^2 - 3x - 2 = 0 \) using the quadratic formula.

\( x = \frac{3 \pm \sqrt{25}}{4} \) \( x = \frac{-3 \pm \sqrt{25}}{4} \) \( x = \frac{3 \pm \sqrt{13}}{4} \) \( x = \frac{-3 \pm \sqrt{13}}{4} \)

9. If the discriminant is zero, the quadratic equation has:

Two complex roots Two irrational roots One real root No solution

10. Solve \( x^2 - 2x - 3 = 0 \) using the quadratic formula.

\( x = 3, x = -1 \) \( x = -3, x = 1 \) \( x = 2 \pm \sqrt{3} \) \( x = -2 \pm \sqrt{3} \)