Exploring the Quadratic Formula and Discriminant

What is the quadratic formula used to solve?

• Quadratic equations

• Cubic equations

• Linear equations

• Exponential equations

In the quadratic formula, what does 'a' represent?

• The coefficient of x

• The coefficient of x squared

• The discriminant

• The constant term

What is the first step in solving a quadratic equation using the quadratic formula?

• Finding the value of the discriminant

• Identifying the coefficients a, b, and c

• Simplifying the equation

• Graphing the equation

If the discriminant (b² - 4ac) is zero, how many real roots does the quadratic equation have?

• None

• One

• Two

• Infinite

What type of roots does a quadratic equation have if the discriminant is negative?

• One real root

• Two complex roots

• Two real irrational roots

• Two real rational roots

In the example where a = 3, b = 5, and c = 1, what is the simplified form of the solution?

• x = -5 ± √13 / 1

• x = -5 ± √13 / 2

• x = -5 ± √13 / 6

• x = -5 ± √13 / 3

What does the discriminant tell us about the roots of a quadratic equation?

• The sum of the roots

• The product of the roots

• The number and type of roots

• The vertex of the parabola

If the discriminant is a positive perfect square, what type of roots will the quadratic equation have?

• Two real irrational roots

• One real root

• Two complex roots

• Two real rational roots

In the example where a = 2, b = -6, and c = 9, what is the value of the discriminant?

• 36

• 0

• -36

• 72

What is the final form of the solution for the quadratic equation where a = 2, b = -6, and c = 9?

• 3 ± 3i / 2

• 3 ± 3i / 4

• 3 ± 3i / 6

• 3 ± 3i / 8