Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros −6 and 1 + i.

Step-by-step explanation:

Complex numbers:

The most important relation when dealing with complex numbers is that:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.

Q has degree 3 and zeros −6 and 1 + i.

Complex roots are always complex-conjugate, which means that if 1 + i is a root, 1 - i is also a root.

I am going to say that the leading coefficient is 1. So

The polynomial is:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15