Mastering Quadratic Equations with the Quadratic Formula

What is the first step in solving a quadratic equation by factorizing?

• Find two numbers that multiply to the coefficient of x.

• Find two numbers that add to the coefficient of x.

• Find two numbers that multiply to the constant term.

• Find two numbers that add to the constant term.

What are the solutions to the equation x^2 + 7x + 10 = 0?

• x = 1 or x = 10

• x = -2 or x = -5

• x = -1 or x = -10

• x = 2 or x = 5

Why might factorizing not work for some quadratic equations?

• Because the numbers are too large.

• Because the equation has no real solutions.

• Because the equation is not in standard form.

• Because there are no two numbers that multiply to the constant term and add to the coefficient of x.

What is the quadratic formula?

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / 2a

What is the discriminant in the quadratic formula?

• b^2 - 4ac

• b^2 + 4ac

• b^2 - 2ac

• b^2 + 2ac

In the quadratic formula, what does the discriminant tell us?

• The number of solutions.

• The type of solutions (real or complex).

• The sum of the solutions.

• The product of the solutions.

What are the solutions to the equation 3x^2 + 5x + 1 = 0 using the quadratic formula?

• x = (5 ± √13) / 6

• x = (5 ± √13) / 3

• x = (-5 ± √13) / 3

• x = (-5 ± √13) / 6

What is the first step in applying the quadratic formula?

• Identify a, b, and c.

• Square root the discriminant.

• Solve for x.

• Calculate the discriminant.

What is the discriminant of the equation x^2 + 7x + 3 = 0?

• 37

• 49

• 25

• 12

What are the solutions to the equation 7x^2 + x - 3 = 0 using the quadratic formula?

• x = (-1 ± √85) / 7

• x = (1 ± √85) / 14

• x = (1 ± √85) / 7

• x = (-1 ± √85) / 14