ALG2 3.3 - Solving Quadratics Using Square Roots

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to solve a quadratic equation using square roots?

Back

Solving a quadratic equation using square roots involves isolating the x² term and then taking the square root of both sides to find the values of x.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x. For example, √9 = 3 because 3² = 9.

Front

How do you solve (x - 2)² = 49?

Back

Take the square root of both sides: x - 2 = ±7. Then solve for x: x = 9 or x = -5.

Front

What are the solutions to (x + 6)² = 49?

Back

x = 7 or x = -13.

Front

What is the first step in solving 5b² - 4 = 41?

Back

Add 4 to both sides to isolate the b² term: 5b² = 45.

Front

How do you isolate b² in the equation 5b² = 45?

Back

Divide both sides by 5: b² = 9.

Front

What are the solutions to b² = 9?

Back

b = 3 or b = -3.

Front

What does it mean if an equation has no real solution?

Back

It means that there are no values of the variable that satisfy the equation, often occurring when taking the square root of a negative number.

Front

What is the solution to the equation x² = -16?

Back

No real solution, since the square root of a negative number is not defined in the set of real numbers.