A polynomial function P(x) has roots of 2, -1 + i, and -1-i when P(x) = 0

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ZMS

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A polynomial function P(x) has roots of 2, -1 + i, and -1-i when P(x) = 0
a) What is the value of i? It is an imaginary number. Look it up.
b) What is the expanded equation of P(x)?
c) Where does P(x) touch the x-axis?

My teacher briefly went over what i is, but I cannot understand it. Can someone explain to me how I would solve these questions?

Thank you!
 
ZMS said:
A polynomial function P(x) has roots of 2, -1 + i, and -1-i when P(x) = 0
a) What is the value of i? It is an imaginary number. Look it up.
b) What is the expanded equation of P(x)?
c) Where does P(x) touch the x-axis?

My teacher briefly went over what i is, but I cannot understand it. Can someone explain to me how I would solve these questions?

Thank you!
Click to expand...
Regarding the definition of i, part (a) instructs you to "look it up". You did that, yes?

What is it about the definition that you don't understand? Please be specific.

For part (b), if R is a root of a polynomial, then x-R is a factor of the polynomial.

Here's an example: the roots of a polynomial are -7 and 4.

This means the factors of the polynomial are (x+7)*(x-4).

We get the expanded form of the polynomial by multiplying out the factors:

x^2 + 3x - 28

X-intercepts occur wherever the polynomial equals zero. Well, a polynomial equals zero at its roots. That's the definition of a root (i.e., a value of x that causes the polynomial to evaluate to zero). :cool:
 
ZMS said:
A polynomial function P(x) has roots of 2, -1 + i, and -1-i when P(x) = 0
a) What is the value of i? It is an imaginary number. Look it up.
b) What is the expanded equation of P(x)?
c) Where does P(x) touch the x-axis?

My teacher briefly went over what i is, but I cannot understand it. Can someone explain to me how I would solve these questions?
Click to expand...
To learn how to find a polynomial from its roots, try here. Once you have studied at least two lessons from the list, please attempt the exercise.

If you get stuck, you can then reply with a clear listing of your thoughts and efforts so far, starting with how you created the corresponding factors and multiplied together the two complex-number ones. Thank you! ;)
 
If a, b, c, and d are roots of the polynomial P then P(x)= q(x- a)(x- b)(x- c)(x- d) for some number q.
 
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