4-4 Assess - 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 square roots?

Back

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

Front

What is the square root of a negative number?

Back

The square root of a negative number is not a real number; it is an imaginary number, represented as i√|a|.

Front

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

Back

A quadratic equation has real solutions if the discriminant (b² - 4ac) is greater than or equal to zero.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

Solve for k: k² - 6 = 43

Back

k = 7, k = -7

Front

Solve for r: 3 + 9r² = 12

Back

r = 1, r = -1

Front

Solve for x: 3x² - 27 = 0

Back

x = 3, x = -3

Front

Solve for x: (x + 6)² = 49

Back

x = 1, x = -13

Front

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

Back

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