anonymous
  • anonymous
Show that the equation has a root in the given interval. -x^4+3x^2+5=0 [2,3]
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Plug in 2, and then 3. The sign of the function will change. That means it's cut the x-axis at least once, and so there is at least one real root in that interval.
anonymous
  • anonymous
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anonymous
  • anonymous
f(2) = 1 f(3) = -49 Look at the graph between x=1 and x=3, you'll see it shoots straight down.

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anonymous
  • anonymous
Am I plugging it as this: f(2) = (-2)^4 + 3(2)^2 +5
anonymous
  • anonymous
No. \[f(2)=-(2)^4+3(2)^2+5=-16+12+5=1\]
anonymous
  • anonymous
You replace x with 2, not -2.
anonymous
  • anonymous
Same for 3:\[f(3)=-(3)^4+3(3)^2+5=-81+27+5=-49\]
anonymous
  • anonymous
Okay, Jennifer?
anonymous
  • anonymous
I have to log off. Just be careful when you sub. numbers in for x...
anonymous
  • anonymous
Okay, th anks

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