Roots of Polynomials

Front

What are the roots of the polynomial equation (x - 3)(x + 6) = 0?

Back

The roots are x = 3 and x = -6.

Front

What are the roots of the equation y = x^2?

Back

The root is x = 0.

Front

Solve for the values of x in the equation (x - 5)(x - 1) = 0.

Back

The roots are x = 5 and x = 1.

Front

Find the roots of the polynomial n(x) = x^3 - 2x^2 - 8x.

Back

The roots are x = 0, x = -2, and x = 4.

Front

Which equation has the solutions x = 5 and x = -7?

Back

The equation is (x - 5)(x + 7) = 0.

Front

Define a polynomial root.

Back

A root of a polynomial is a value of x that makes the polynomial equal to zero.

Front

What is the degree of the polynomial n(x) = x^3 - 2x^2 - 8x?

Back

The degree is 3.

Front

Explain the Factor Theorem.

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

Front

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

Back

The roots of a polynomial correspond to the values of x that make each factor equal to zero.

Front

How do you find the roots of a quadratic equation?

Back

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