Finding Real Irrational Roots with the Quadratic Formula

What is the first step to solve a quadratic equation when it is not factorable?

• Complete the square

• Try to factorize again

• Use the quadratic formula

• Evaluate the discriminant

Why is it important to identify a, b, and c in a quadratic equation?

• To check if the equation is linear

• To apply the quadratic formula correctly

• To simplify the equation further

• To determine the graph of the equation

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

• Whether the roots are real or complex

• How to factorize the equation

• The exact values of the roots

• The number of solutions to the equation

What is the formula for the discriminant of a quadratic equation?

• 2a - b^2

• b^2 + 4ac

• 4ac - b^2

• b^2 - 4ac

If the discriminant is a perfect square, what can be said about the roots?

• The roots do not exist

• The roots are rational

• The roots are irrational

• The roots are complex

What happens if the discriminant is less than zero?

• The equation is not quadratic

• The equation has no real roots

• The equation has two real roots

• The equation has one real root

How can the square root of 40 be simplified using square numbers?

• 4√5

• 5√8

• 6√6.67

• 2√10

What is the result of the quadratic formula when a = 3, b = 8, and c = 2?

• -8 ± 2√10 / 6

• -4 ± 2√10 / 3

• -8 ± √40 / 6

• -4 ± √10 / 3

What does it mean if the discriminant equals zero?

• The quadratic equation has exactly one real root

• The quadratic equation has two distinct real roots

• The quadratic equation has no real roots

• The quadratic equation has two identical complex roots

What is the purpose of factoring out the greatest square number from under the square root when simplifying the result of the quadratic formula?

• To change the coefficients of the equation

• To convert complex roots to real roots

• To increase the value of the discriminant

• To simplify the square root for easier calculation