A few question about finding zeros in polynomials?

Question

I am wondering just a few things about this and my teacher can't seem to explain it AT ALL!

First: Is there a difference between "finding the zeros" and "finding all REAL zeros"?
Second: why can't I just use my graphing calculator to just see where the line crosses the X-Axis all the time?
Third: What is an Upper or Lower bound zero??!

Answer 1

1) Some polynomials have complex zeros which are not real zeros.

2) Your calculator will find approximate values for the real zeros. However, it will not find exact values in all cases and it will not find complex zeros.

3) Not certain what is meant here. Possibly the greatest (real) zero and least (real) zero, but I can't say for sure.

Answer 2

to address the first commenter, the square root of 56 is most certainly a real number.



First: Yes, there is a difference. Your teacher should be able to tell you if you need to find all zeros (more commonly called roots), or all real zeros. If she/he can't, they're not a real math teacher.



Second, You can, at least for real roots. This is, for example, the only way to find a zero of an equation like e^x - x - 2 = 0.



Third: No idea. That's not a math phrase.

Answer 3

First: Zeros could be real numbers or complex numbers (with square root of -1). For example, a n-th degree may have a maximum of n crossing points with x-axis but it may not, meaning it has some complex roots. So number of real zeros is less or equal to the degree while number of zeros (including complex) is always the degree

Second: Complex numbers can't be shown on the graph calculator

Third: Based on synthetic division, you can find the upper and lower bounds of zeros, meaning you are certain that the "real" zeros are within a range. for example, if z_i are your zeros, you can find x1 and x2 guaranteeing that x1
YOu may refer the following link for explanation of synthetic division



http://laurashears.info/math121/lecture_notes/unit5/Upper%20and%20Lower%20bounds/

Answer 4

Yes, there is a difference. Sometimes, a zero of a polynomial might be the square root of fifty-six. This is not a real number.



Second: perhaps the answer will be a fractional value or radical value, when the calculator will spit out a decimal. You want to get the problem right.



Third: Honestly, I can't answer that.

Answer 5

I start up those with the help of finding for evident roots. There are no. attempt multiple integer values, beginning from 0 and dealing left and perfect. There seem to be roots merely wanting x = a million; someplace between x = a million and x = 2; between x = 2 and x = 3; and between x = -2 and x = -a million. With no longer something functional having regarded, factoring and artificial branch won't artwork; the only selection is to grind them out employing Newton new launch -- that's extra artwork than I love to do perfect now.