Question

Show that the equation has a root in the given interval.

-x^4+3x^2+5=0 [2,3]

Answer 1

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.

Answer 2

f(2) = 1
f(3) = -49

Look at the graph between x=1 and x=3, you'll see it shoots straight down.

Answer 3

Am I plugging it as this: f(2) = (-2)^4 + 3(2)^2 +5

Answer 4

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

Answer 5

You replace x with 2, not -2.

Answer 6

Same for 3:\[f(3)=-(3)^4+3(3)^2+5=-81+27+5=-49\]

Answer 7

Okay, Jennifer?

Answer 8

I have to log off. Just be careful when you sub. numbers in for x...

Answer 9

Okay, th anks