solve quadratics by 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 method can be used to solve a quadratic equation when it can be expressed as a perfect square?

Back

The method used is to take the square root of both sides of the equation.

Front

How do you isolate x in the equation x² = k?

Back

To isolate x, take the square root of both sides: x = ±√k.

Front

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

Back

The solutions are x = 5/2 and x = -5/2.

Front

What is the square root of 64?

Back

The square root of 64 is ±8.

Front

How do you solve the equation (h - 2)² = 9?

Back

Take the square root of both sides: h - 2 = ±3, leading to h = 5 or h = -1.

Front

What is the first step in solving the equation 3x² - 27 = 0?

Back

The first step is to add 27 to both sides: 3x² = 27.

Front

What is the value of x when solving the equation 3x² = 27?

Back

Divide both sides by 3 to get x² = 9, then take the square root: x = ±3.

Front

What does it mean for an equation to be a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.