Solve Quadratics by Taking 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

It means isolating the x² term and then applying the square root to both sides of the equation 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.

Front

Solve for x: 3x² = -48

Back

no real solution

Front

Solve for x: (x - 4)² + 8 = 33

Back

x = -1, 9

Front

Solve for x: x² - 16 = 0

Back

x = ± 4

Front

Solve for x: -7(x + 3)² + 63 = 0

Back

x = -6, 0

Front

Solve for x: x² = 49

Back

x = ± 7

Front

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

Back

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

Front

What is the discriminant in a quadratic equation?

Back

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