Conjugate Root Theorem

Front

What is the Complex Conjugate Root Theorem?

Back

The Complex Conjugate Root Theorem states that if a polynomial has real coefficients and a complex root (a + bi), then its complex conjugate (a - bi) is also a root.

Front

If 3 + 5i is a root of a polynomial, what is another root?

Back

3 - 5i

Front

If -7i is a root of a polynomial, what is another root?

Back

7i

Front

How do you express a polynomial in factored form given roots 7 and -2i?

Back

(x - 7)(x + 2i)(x - 2i)

Front

What is the factored form of 27x^3 + 8?

Back

(3x + 2)(9x^2 - 6x + 4)

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What does it mean for a polynomial to have real coefficients?

Back

A polynomial has real coefficients if all the coefficients (the numbers in front of the variables) are real numbers.

Front

What is a root of a polynomial?

Back

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