Simplifying radicals and Quadratic Formula

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify √28?

Back

√28 = √(4*7) = √4 * √7 = 2√7.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant indicates the nature of the roots of a quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, two imaginary roots.

Front

If the discriminant is positive, what can we say about the roots?

Back

There are two distinct real solutions.

Front

If the discriminant is zero, what can we say about the roots?

Back

There is one real solution with a multiplicity of 2.

Front

If the discriminant is negative, what can we say about the roots?

Back

There are two imaginary solutions.

Front

What is the value of the discriminant for the equation x² + 7x + 13?

Back

The discriminant is -3, indicating two imaginary roots.

Front

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

Back

Calculate the discriminant (b² - 4ac). If it is non-negative, the equation has real solutions.

Front

What is the simplified form of √(49)?

Back

√(49) = 7.