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 squared term and then taking the square root of both sides to find the variable's values.

Front

What is the square root property?

Back

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

Front

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

Back

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

Front

Solve: (x + 4)² = 36

Back

x = 2, -10

Front

What is the first step in solving 2(w + 1)² = 72?

Back

Divide both sides by 2 to isolate the squared term: (w + 1)² = 36.

Front

Solve: 3x² = 12

Back

x = ±2.

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed as a + bi, where i is the imaginary unit.

Front

Solve for y: 3y² - 4 = 287

Back

y = √97, -√97.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.