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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

• 2a - b^2

• b^2 + 4ac

• 4ac - b^2

• b^2 - 4ac

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B

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

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CCSS.HSA-REI.B.4B