Solve Quadratic by Square Root

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 is the square root property in solving quadratic equations?

Back

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

Front

How do you isolate the variable in a quadratic equation before applying the square root method?

Back

To isolate the variable, you need to move all terms to one side of the equation, setting it equal to zero or isolating the squared term.

Front

What is the first step in solving the equation 3 - 9r² = 12?

Back

The first step is to isolate the term with the variable: -9r² = 12 - 3, which simplifies to -9r² = 9.

Front

What are the solutions to the equation (x - 7)² + 4 = 40?

Back

The solutions are x = 1 and x = 13.

Front

How do you solve k² - 6 = 43 using square roots?

Back

First, isolate k²: k² = 43 + 6 = 49. Then take the square root: k = ±7.

Front

What does it mean to find the roots of a quadratic equation?

Back

Finding the roots of a quadratic equation means determining the values of the variable that make the equation equal to zero.

Front

What is the solution to the equation x² - 5 = 31?

Back

The solution is x = ±6.

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

What is the significance of the discriminant in quadratic equations?

Back

The discriminant helps to determine the nature and number of solutions of a quadratic equation.