Solving Quadratics Using Square Roots and Factoring

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?

Back

To solve a quadratic equation means to find the values of x that make the equation true, i.e., the roots of the equation.

Front

What is the square root property in solving quadratics?

Back

The square root property states that if x² = k, then x = ±√k.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of rewriting a quadratic equation as a product of two binomials.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two real solutions, one real solution, or no real solutions.

Front

How do you determine if a quadratic equation has real solutions?

Back

You can determine if a quadratic equation has real solutions by calculating the discriminant (b² - 4ac). If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if negative, there are no real solutions.

Front

Solve: 3x² = -60

Back

No Real Number Solution.

Front

Solve: x² + 5x - 14 = 0

Back

x = 2, x = -7.

Front

Solve: x² - 10 = -10

Back

x = 0.