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 9?

Back

±3

Front

If x² = 1, what are the possible values of x?

Back

x = ±1

Front

What is the principle of taking square roots in equations?

Back

When taking the square root of both sides of an equation, consider both the positive and negative roots.

Front

How do you simplify √(a²)?

Back

√(a²) = |a|, which means the absolute value of a.

Front

What is the solution to the equation x² = 16?

Back

x = ±4

Front

What is the first step in solving x² = 25?

Back

Isolate x² to get x² = 25.

Front

What does it mean if a quadratic equation has no real solution?

Back

It means that the equation's discriminant (b² - 4ac) is less than zero, indicating that the roots are complex.

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.