Solving Quadratic Equations with Square Roots

Betsy introduces quadratic equations, focusing on solving them using square roots. She explains the concept of quadratic equations, identifies common features, and demonstrates solving methods through examples like x^2 = 36, x^2 = 8, and 3x^2 = 36. Betsy also discusses cases with no real solutions, such as x^2 = -16 and 12x^2 = -4, and highlights the importance of isolating x^2 and handling negative numbers. The session concludes with a preview of solving quadratic equations using factoring.

What is the degree of a quadratic equation?

• 2

• 4

• 1

• 3

What are the solutions to the equation x^2 = 36?

• 0

• 6 and -6

• 18

• 36

How do you simplify the square root of 8?

• 2

• √8

• 4√2

• 2√2

What is the result of x^2 = -16 in real numbers?

• 4 and -4

• -4

• No real solutions

• 16

How do you isolate x^2 when the equation is 3x^2 = 36?

• Subtract 3

• Add 3

• Multiply by 3

• Divide by 3

What is the simplified form of the square root of 12?

• 12

• √12

• 3√4

• 2√3

What does x^2 = -20 simplify to when divided by -2?

• x^2 = 20

• x^2 = -20

• x^2 = -10

• x^2 = 10

What are the roots of the equation x^2 = 10?

• 10

• No real roots

• ±10

• ±√10

What happens to the equation 12x^2 = -4 when divided by 12?

• x^2 = -2

• x^2 = 2

• x^2 = -1/3

• x^2 = 1/3

What is the correct approach to solve 3x^2 = 36 for x?

• None of the above

• Multiply by 3, then take the square root

• Divide by 3, then take the square root

• Take the square root directly