What is a “real” zero?
1. A solution to a polynomial.
2. A non-imaginary number.
3.An x-intercept of a polynomial.
4. All of the above.
The answer is 4, right?
This is a nutty question.
a "real" zero is a solution to a plynomial whch is equal to zero.
If poly(x)=0, then a real zero is a real (not complex) value of x which satisfies the equation.
So 1. would be a good answer, but it should say "a real solution that makes the polynomial value zero.
2. would be ok, but is should say "a number that does not contain an imaginary value"
3. might be right, but the x axis has to be a real number axis, and in graphing polynomials, there is no requirement it has to be plotted on a real number plane.
4. could be right.
So I guess I assume your teacher is just sloppy with language, and teaching you to do the same. Go with 4. But it is important to understand what I said on each answer.
Yes, the answer is 4. A "real" zero refers to a value that satisfies the equation or condition specified in the given options (1, 2, and 3).
1. A solution to a polynomial: A real zero is also known as a root or a solution to a polynomial equation. It is a value of the variable that makes the polynomial equation equal to zero.
2. A non-imaginary number: In mathematics, imaginary numbers are those that involve the square root of negative one (i). Real numbers are those that do not involve the imaginary unit. So, a real zero is a non-imaginary number.
3. An x-intercept of a polynomial: An x-intercept is a point where a polynomial curve intersects the x-axis. At this point, the y-coordinate is zero, which means the function value is zero. Hence, an x-intercept is another term for a real zero.
Therefore, since the definition of a "real" zero includes all three options, the correct answer is 4, which states "all of the above."