ckallerid
  • ckallerid
How many zeros does the function f(x) = 4x11 − 20x7 + 2x3 − 15x + 14 have? 11 7 5 3
Mathematics
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SOLVED
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katieb
  • katieb
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whpalmer4
  • whpalmer4
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
  • ckallerid
@whpalmer4 Highest power of the variable. So it's 11 right?
whpalmer4
  • whpalmer4
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 (\(a\pm bi\))

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ckallerid
  • ckallerid
oki thanks!

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