Solving Quadratics by 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 by square roots?

Back

Solving a quadratic equation by 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 first step in solving the equation 3x² - 27 = 0?

Back

The first step is to isolate the x² term by adding 27 to both sides, resulting in 3x² = 27.

Front

How do you isolate x² in the equation 5b² - 4 = 41?

Back

Add 4 to both sides to get 5b² = 45, then divide by 5 to isolate b², resulting in b² = 9.

Front

What is the square root of 9?

Back

The square root of 9 is ±3.

Front

What are the solutions to the equation 4x² - 25 = 0?

Back

The solutions are x = ±5/2.

Front

What is the significance of the ± symbol in solutions?

Back

The ± symbol indicates that there are two possible solutions: one positive and one negative.

Front

How do you solve the equation 5m² + 1 = 6?

Back

First, subtract 1 from both sides to get 5m² = 5, then divide by 5 to get m² = 1, and finally take the square root to find m = ±1.

Front

What is the general form of a quadratic equation?

Back

The general form is ax² + bx + c = 0.

Front

What is the value of x in the equation 3x² - 27 = 0?

Back

The value of x is ±3.