Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

The quadratic has 2 Complex Solutions.

Front

Simplify the expression: -3√80a^7

Back

-12a³√5a

Front

Solve the quadratic equation: x^2 - 5x + 10 = 0

Back

The solutions are (5 - i√15)/2 and (5 + i√15)/2.

Front

What does a discriminant of 0 indicate about the solutions of a quadratic equation?

Back

The quadratic has 1 Rational Solution.

Front

Rationalize the denominator of \( \frac{\sqrt{5}}{2\sqrt{3}} \)

Back

The result is \( \frac{\sqrt{15}}{6} \).

Front

What is the quadratic formula?

Back

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

Define the term 'discriminant' in the context of quadratic equations.

Back

The discriminant is the expression \( b^2 - 4ac \) that determines the nature of the roots of the quadratic equation ax^2 + bx + c = 0.

Front

What are the possible types of solutions for a quadratic equation based on the discriminant?

Back

1. 2 Rational Solutions (discriminant > 0) 2. 1 Rational Solution (discriminant = 0) 3. 2 Complex Solutions (discriminant < 0)

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula \( (h, k) \) where \( h = -\frac{b}{2a} \) and \( k = f(h) \).

Front

What is the standard form of a quadratic equation?

Back

The standard form is \( ax^2 + bx + c = 0 \) where a, b, and c are constants.