Question

Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 7- i, and passing through the origin P(x)=

Answer 1

zeros i and 7- i,

Non-real roots appear in conjugate pairs.

If i is a root, then so is -i

If 7- i is a root, then so is 7 + 1

That is a total of 4 roots.

If the polynomial is of degree 5, there is a fifth root.

Because the polynomial passes through the origin, then x = 0 is the fifth root.

Answer 2

If x = 0 is a root, then x - 0 or x is a factor.

If x = i is a root, then x - i is a factor.

If x = -i is a root, then x + i is a factor.

If x = 7 - i is a root, then x - 7 + i is a factor.

If x = 7 + i is a root, then x - 7 - i is a factor.

Answer 3

The polynomial is the product of these 5 factors.

P(x) = x * (x - i ) * (x + i) * (x - 7 + i) * ( x - 7 - i)

Your Task: Multiply those factors and simplify. @aprilrod23

Then, there's the matter of integer coefficient.

Answer 4

@aprilrod23

Let an online program do all that multiplication if that is allowed.

Go to wolframalpha.com and enter:

x(x-i) (x+i)(x -7+i)( x-7-i)=

After the "Wolf" calculates, scroll down and look at the alternate forms of writing the product.

Post what you get, okay?

Answer 5

@aprilrod23 --> is just looking around

Answer 6

thank you I got the answer