How many zeros does the function f(x) = 4x11 − 20x7 + 2x3 − 15x + 14 have?
11
7
5
3

Question

How many zeros does the function f(x) = 4x11 − 20x7 + 2x3 − 15x + 14 have?
 11
 7
 5
 3

whpalmer4 · Answer

You always have as many zeros as the highest power of the variable in the polynomial.  A quadratic ($x^2$) always has 2, a cubic ($x^3$) has 3, etc.

Sometimes you will have a smaller number of unique zeros.  For example, $$x^2=0$$has two zeros, but they are both $x = 0$.

ckallerid · Answer

@whpalmer4 Highest power of the variable. So it's 11 right?

whpalmer4 · Answer

Yes, that's right.  And at no extra charge, here are the approximate values:

-1.52372
0.7799
1.49728
-0.905024-0.497208i
-0.905024+0.497208i
-0.140148-1.05849i
-0.140148+1.05849i
0.0233478 -1.45963i
0.0233478 +1.45963i
0.645095 -0.585822i
0.645095 +0.585822i

Notice how a bunch of them are complex numbers ($a + bi, \text{ where }i = \sqrt{-1}$) and come in conjugate pairs ($a\pm bi$)

ckallerid · Answer

oki thanks!