M5.1-5.2: Solving Polynomial Equations

Front

Identify the values of a, b, and c in the quadratic equation: 3x² - 8x + 15 = 0

Back

a = 3, b = -8, c = 15

Front

What is the greatest number of solutions that a Quadratic Equation can have?

Back

2

Front

What determines the end behavior of a polynomial function?

Back

The degree and the sign of the leading coefficient.

Front

Identify the degree and the sign of the leading coefficient for the polynomial: 4x³ - 2x² + 5.

Back

Degree - Odd, Leading Coefficient Positive

Front

What are the roots of the function f(x) = (x - 2)(x + 3)?

Back

x = 2 or x = -3

Front

What is the leading coefficient of the polynomial written in standard form: -x² + 4x - 7?

Back

-1

Front

Define a polynomial equation.

Back

An equation that involves a polynomial expression, which is a sum of terms, each consisting of a variable raised to a non-negative integer power and multiplied by a coefficient.

Front

What is the standard form of a quadratic equation?

Back

ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the discriminant in a quadratic equation and what does it indicate?

Back

The discriminant is b² - 4ac; it indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you find the roots of a quadratic equation using factoring?

Back

Set the equation to zero and factor it into the form (x - p)(x - q) = 0, then solve for x = p and x = q.