2x^3 + x^2 - 5= 0
x=?
Is this possible to solve?
3 answers
Yea. x=1.209355. You have to find the roots.
Thank you, but how you made that? What was the process?
There is no "nice" formula for solving cubics.
We can graph y = 2x^3 + x^2 - 5 and get an approximate answer form the graph
http://www.wolframalpha.com/input/?i=plot+y+%3D+2x%5E3+%2B+x%5E2+-+5
and "guess" at appr 1.2
You can nibble away at the answer using a calculator
x = 1, y = 2+1-5 = -2 , too low
x = 1.2 , y = -.0104 , a bit too low but close
x = 1.21, y = .00722 , a bit too high but very close
x = 1.205 , y = -.048 , a bit too low but close
so x is between 1.205 and 1.21
you get the idea ?
If you know Calculus, use Newton's method.
let me know if you study Calculus before I show you that method
We can graph y = 2x^3 + x^2 - 5 and get an approximate answer form the graph
http://www.wolframalpha.com/input/?i=plot+y+%3D+2x%5E3+%2B+x%5E2+-+5
and "guess" at appr 1.2
You can nibble away at the answer using a calculator
x = 1, y = 2+1-5 = -2 , too low
x = 1.2 , y = -.0104 , a bit too low but close
x = 1.21, y = .00722 , a bit too high but very close
x = 1.205 , y = -.048 , a bit too low but close
so x is between 1.205 and 1.21
you get the idea ?
If you know Calculus, use Newton's method.
let me know if you study Calculus before I show you that method