Solving Quadratics by Taking Square Roots

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is 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 taking square roots?

Back

Solving a quadratic equation by taking square roots involves isolating the x² term and then applying the square root to both sides of the equation, resulting in two possible solutions: x = ±√(value).

Front

What is the square root of 64?

Back

The square root of 64 is 8, and since we consider both positive and negative roots, the solutions are x = 8 and x = -8.

Front

How do you isolate x² in the equation 3x² - 27 = 0?

Back

To isolate x², first add 27 to both sides to get 3x² = 27, then divide both sides by 3 to obtain x² = 9.

Front

What are the solutions to the equation x² = 9?

Back

The solutions to the equation x² = 9 are x = 3 and x = -3.

Front

What is the first step in solving the equation 5m² + 1 = 6?

Back

The first step is to subtract 1 from both sides to isolate the term with m², resulting in 5m² = 5.

Front

How do you solve for m in the equation 5m² = 5?

Back

Divide both sides by 5 to get m² = 1, then take the square root of both sides to find m = ±1.

Front

What is the process to solve the equation 4m² - 100 = 0?

Back

First, add 100 to both sides to get 4m² = 100, then divide by 4 to obtain m² = 25, and finally take the square root to find m = ±5.

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

What is the relationship between the coefficients a, b, and c in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.