Flashcard 18 Practice- Solving with 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 if a quadratic equation has no real solution?

Back

A quadratic equation has no real solution if the discriminant (b² - 4ac) is less than zero.

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation by taking square roots, isolate the x² term and then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the square root of a negative number?

Back

The square root of a negative number is an imaginary number, represented as i√|x|, where i is the imaginary unit.

Front

How do you simplify square roots?

Back

To simplify square roots, factor the number under the square root into its prime factors and look for pairs of factors.

Front

What is the solution to the equation x² = 16?

Back

The solutions to the equation x² = 16 are x = 4 and x = -4.

Front

What is the process for solving (x + 4)² = 36?

Back

To solve (x + 4)² = 36, take the square root of both sides, resulting in x + 4 = 6 or x + 4 = -6, then solve for x.

Front

What is the value of √40 simplified?

Back

The value of √40 simplified is 2√10.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.