Solving Quadratics by Square Roots

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 does it mean to solve a quadratic equation by taking square roots?

Back

Solving a quadratic equation by taking square roots involves isolating the squared term and then applying the square root to both sides of the equation.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x. It can be positive or negative.

Front

How do you isolate a squared term in a quadratic equation?

Back

To isolate a squared term, you move all other terms to the opposite side of the equation.

Front

Solve by taking square roots: 5m² + 1 = 6

Back

m = 1 or -1

Front

Solve using square roots: k² - 6 = 43

Back

k = 7, k = -7

Front

What is the solution to the equation 3x² - 27 = 0?

Back

x = 3, -3

Front

Solve using square roots: x² = 9

Back

x = ±3

Front

What is the principle of taking square roots in solving equations?

Back

The principle states that if x² = a, then x = ±√a.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.