U3 Flashcard 1 Review

Front

Solve the equation: 4m^2 - 100 = 0

Back

m = 5, -5

Front

Why are there NO REAL SOLUTIONS for certain quadratic equations?

Back

Because we cannot take the square root of a negative number.

Front

Multiply: (4 + \sqrt{2})(4 - \sqrt{2})

Back

14

Front

What is the value of \frac{2}{\sqrt[3]{10}}?

Back

\frac{\sqrt[3]{100}}{5}

Front

What is a quadratic equation?

Back

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What does it mean for a quadratic equation to have real solutions?

Back

It means that the solutions (roots) of the equation are real numbers, not complex.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b^2 - 4ac and determines the nature of the roots.

Front

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

Back

There are two distinct real roots.

Front

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

Back

There is exactly one real root (a repeated root).

Front

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

Back

There are no real roots; the roots are complex.