Alg. 2 Solving Quadratics by Square Root

Front

What is the standard form of a quadratic equation?

Back

The standard 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, resulting in two possible solutions: ±√(value).

Front

What is the solution to the equation x² = 25?

Back

x = ±5.

Front

What is the solution to the equation x² = 0?

Back

x = 0.

Front

What is the solution to the equation x² = -16?

Back

No real solution, as the square root of a negative number is not defined in the set of real numbers.

Front

How do you determine if a quadratic equation has real solutions?

Back

A quadratic equation has real solutions if the value under the square root (the discriminant) is non-negative (b² - 4ac ≥ 0).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots.

Front

What is the solution to the equation 4x² = 64?

Back

x = ±4.

Front

What is the solution to the equation x² - 9 = 0?

Back

x = ±3.

Front

What is the solution to the equation k² - 36 = 0?

Back

k = ±6.