Numerical Method Set of questions

[thomas49th]

Hi, I'm currently stuck with 2 questions:

1. Given that the negative root of the equation $$f(x) = x^{3} - 7(x) + 5$$
lies between a and a + 1 where a is an integer write down a value of a

2. Show that the equation $$e^{-x} = x^{2}$$ has a root between x = 0.70 and 0.71

Thanks :)

 

[rock.freak667]

Well for both you need to find values that make f(x) differ in sign..

 

[thomas49th]

do i use trial and error? Or is there a more sophisticated way?

 

[rock.freak667]

For the first one you can just use trial an error with negative values...but I can simply see one negative value of x that will make f(x)= ...

 

[thomas49th]

f(0) = 5
f(1) = -1

so a = 0

 

[rock.freak667]

But you see...between 0 and 1 would mean that the root is +ve so you must find f(-1) or f(-2) etc for the root to be -ve