Exploring the Quadratic Formula and Discriminant

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 + b = 0

In the quadratic equation ax^2 + bx + c = 0, what do the letters a, b, and c represent?

• Exponents

• Constants

• Coefficients

• Variables

What is the quadratic formula used to find the solutions of a quadratic equation?

• x = (-b ± √(b^2 - 4ac)) / a

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

What does the discriminant (b^2 - 4ac) determine in a quadratic equation?

• The number of solutions

• The type of solutions

• Both the number and type of solutions

• The sum of the solutions

If the discriminant is greater than zero, how many real solutions does the quadratic equation have?

• Infinite

• Two

• None

• One

What is the sum of the solutions to the equation x^2 - 4x - 10 = 0?

• 8

• 6

• 4

• 2

In the equation x^2 - 4x - 10 = 0, what are the values of a, b, and c?

• a = 1, b = -4, c = 10

• a = -1, b = 4, c = -10

• a = 1, b = -4, c = -10

• a = 1, b = 4, c = -10

For the equation 3x^2 - 6x + c = 0 to have exactly one real solution, what must the value of c be?

• 1

• 2

• 4

• 3

What condition must the discriminant meet for a quadratic equation to have exactly one real solution?

• None of the above

• Equal to zero

• Less than zero

• Greater than zero

If the discriminant is less than zero, what type of solutions does the quadratic equation have?

• No solutions

• No real solutions, but two complex solutions

• One real solution

• Two real solutions