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anonymous

  • 5 years ago

Show that the equation has a root in the given interval. -x^4+3x^2+5=0 [2,3]

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  1. anonymous
    • 5 years ago
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    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.

  2. anonymous
    • 5 years ago
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  3. anonymous
    • 5 years ago
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    f(2) = 1 f(3) = -49 Look at the graph between x=1 and x=3, you'll see it shoots straight down.

  4. anonymous
    • 5 years ago
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    Am I plugging it as this: f(2) = (-2)^4 + 3(2)^2 +5

  5. anonymous
    • 5 years ago
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    No. \[f(2)=-(2)^4+3(2)^2+5=-16+12+5=1\]

  6. anonymous
    • 5 years ago
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    You replace x with 2, not -2.

  7. anonymous
    • 5 years ago
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    Same for 3:\[f(3)=-(3)^4+3(3)^2+5=-81+27+5=-49\]

  8. anonymous
    • 5 years ago
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    Okay, Jennifer?

  9. anonymous
    • 5 years ago
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    I have to log off. Just be careful when you sub. numbers in for x...

  10. anonymous
    • 5 years ago
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    Okay, th anks

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