Roots / Factors

Front

What is another word for zeros?

Back

roots

Front

Use the graph to determine the solutions: What are the x-intercepts?

Back

1 and 3

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

0, 6, -5

Front

What is another word for zeros?

Back

All of these! (solutions, x-intercepts, roots)

Front

Define 'roots' in the context of polynomial functions.

Back

Roots are the values of x for which the polynomial equals zero.

Front

What is the relationship between roots and factors of a polynomial?

Back

If r is a root of a polynomial, then (x - r) is a factor of that polynomial.

Front

How do you find the roots of a quadratic equation?

Back

Use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

Front

What is the significance of the y-intercept in relation to roots?

Back

The y-intercept is the value of the function when x = 0; it does not directly indicate roots.

Front

What does it mean if a polynomial has multiple roots?

Back

It means that the root is repeated, indicating a point of tangency on the graph.

Front

How can you verify the roots of a polynomial?

Back

Substitute the roots back into the polynomial; if the result is zero, they are verified.