Can you help me with some college algebra!? Iam stuck!?

Question

I know the answer because its an example, but it doesnt show me step by step so i dont understand how they get to the answer

Use synthetic division to decide whether 4+i is a zero
of f(x)= xsquared -8x+17

this is the answer: Since f(4+i) equals 0, 4+i is a zero of f(x)=xsquared -8x+17

ohhh! thank you soooo much! : )

Answer 1

Solve f(4+i) by substituting (4+i) for x:

f(4+i) = (4+i)^2 - 8(4+i) + 17

= 16 + 8i + i^2 - 32 - 8i + 17

= 18 + 8i -1 -32 - 8i + 17 (recall that i^2 = -1)

= 0

Therefore (4+i) is a zero of f(x), since f(4+i) = 0

HTH! :-)

Answer 2

I don't know what does the synthetic division mean but:

Replace x with (4+i) =>

f(4+i) = (4+i)squared - 8*(4+i) + 17=
= 4squared + 2*4*i + i squared - 8*4 - 8*i +17=
= 16 + 8*i -1 - 32 - 8*i+17=
= 0

=> f(4+i)=0

* i squared= -1


I hope this can help you. Sorry if I have written a too much easy way, because maybe the "synthetic division" means something else. I'm not English... but if you can explain what does it mean maybe I can help you with another solving method.

Answer 3

yes it is a zero of that equation. hold up, i'll show you.

btw, this is how you write squared: ^2

first you have to try to factor the original equation: x^2 - 8x +17

since this can't be factored by using the FOIL method, you have to use the Quadratic Equation. You should memorize this equation since it can be used to factor any function that can't be factored using the FOIL. Quadratic Equation is: (-b +/- square root of (b^2 - 4 ac))/2a

a, b and c in this equation stand for the 1st 2nd and 3rd term of the original equation, so in this case: 1, -8, 17

so you when plug those numbers into the quadratic equation, you get this result half way through:

(8 +/- square root of -4)/2

since there is no real way of taking the square root of a negative number, mathematicians came up with the concept of imaginary numbers. that's where the term "i" comes in.

so the square root of -4 is "2i".....so you have

(8 +/- 2i)/2

when you solve for that you always get two answers

(8 + 2i)/2, which is 4+i and
(8 - 2i)/2, which is 4-i

those are your two answers, so now you know that 4+i is a zero of the original equation

Answer 4

(4+i)^2 -8(4+i) +17 =
16 +8i +i^2 -32-8i + 17 =
33 -32 -1 = 0.

You want to keep two things in mind:
i^2 = -1
And when you square a binomial, the pattern is
(a+b)^2 = a^2 + 2ab + b^2 or write the binomial down twice and do FOIL.

Answer 5

Here's the actual synthetic division:

4+i|1....-8.....17
...........4+i...-17
--------------------
......1..-4+i....0

Do you understand synthetic division well enough to figure out what's going on from this example, or should I explain further?