Solve Quadratic Equations using 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 using square roots?

Back

Solving a quadratic equation using square roots involves isolating the x² term and then taking the square root of both sides to find the values of x.

Front

Solve: 2x² = 30

Back

x = ±√15

Front

Solve: 2(w + 1)² = 72

Back

w = 5, -7

Front

Solve: x² - 4 = 0

Back

x = ±2

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.

Front

What are the steps to solve a quadratic equation using square roots?

Back

1. Isolate the x² term. 2. Take the square root of both sides. 3. Solve for x, considering both the positive and negative roots.

Front

Solve: 2(x−7)² = 32

Back

x = 3 and 11

Front

Solve: 3x² = -12

Back

x = ±2i (complex solutions)

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.