Question

Find the roots without using calculator 6x^4 - 8x^3 + 1 = 0

Answer 1

everything i can think of involves using a calculator in some way

Answer 2

there is no negative value and there are two positive answers. 1 close to but a lil over .5 and 1 close to but a lil over 1

Answer 3

if u were willing to do the math u can use newtons method using .5 and 1 as ur starting points. u wont get an exact answer but im sure u'll get it as far as u need to. Newton's method:
\[X(n+1)=X(n)+f(x)/f'(x)\]

f(x)=6x^4-8x^3+1
f'(x)=24x^3-24x^2

Answer 4

without using a calculator you can graph this
6x^4 - 8x^3 + 1 = 0

by graphing you get x=0.614 and x=1.25 ans....

Answer 5

or try newtons method as jathoday mention...

Answer 6

i thought graphing itwould b the same as using a calculator. if u can graph it thats the way to go..