8. determine whether the statement is always, sometimes, or never true. a polynomial function with real coefficients has real zeros. (1 point) a. always true b. sometimes true c. never true 9. determine whether the statement is always, sometimes, or never true. a polynomial function that does not intercept the x-axis has complex roots only. (1 point) a. always true b. sometimes true c. never true 10. determine whether the statement is always, sometimes, or never true. an odd degree polynomial function with real coefficients has at least one real root. (1 point) a. always true b. sometimes true c. never true

8. B) sometimes true

9. A) always true

10. A) always true

Step-by-step explanation:

8. A polynomial function with real coefficients has real zeros. This is sometimes true because say we have an equation x^2+10. If you graph this, you will notice that there are no points on the x axis, or no zeroes. That means that this equation would have complex roots. x^2+10 is a real number equation without any complex numbers so the answer is sometimes true.

9. A polynomial function that does not intercept the x-axis has complex roots only. a If a line crosses or touches the x (horizontal) axis on a graph then you can say that the point where it touches is a root. If any equation on a graph does not have a point on the x axis then it has complex roots. So the answer is always true.

10. An odd degree polynomial function with real coefficients has at least one real root. a Think about all the odd degree equations you know. y=x^1 (basically y=x), y=x^3, etc. A linear slope intercept form equation has an odd degree of 1 and passes through the x axis only once. If you plug in x^3 on a graphing calculator or desmos.com/calculator you will see that the y range has infinately many solutions. You can mess with this and plug in whacky equations like x^3-42x^2+16.92x-.4^8; no matter what, there will always be atleast 1 real root, so this is always true.

:)

answer: can and shows the work

step-by-step explanation:

there is no question content here, but you for the free points! : d