SOLUTION: Hi I really need some help in solving this..this is new to me.Any help will be gladly be appreciated. how do you solve f(x)= Xcube minus 4x squared plus 7x minus 2 f(x) =

Algebra ->  Functions -> SOLUTION: Hi I really need some help in solving this..this is new to me.Any help will be gladly be appreciated. how do you solve f(x)= Xcube minus 4x squared plus 7x minus 2 f(x) =      Log On


   

Question 149309: Hi I really need some help in solving this..this is new to me.Any help will be gladly be appreciated.
how do you solve
f(x)= Xcube minus 4x squared plus 7x minus 2
f(x) = (4x - 7) to the power of 20
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
By solve, I assume you mean find the zeros where f(x)=0.
f%28x%29=x%5E3-4x%5E2%2B7x-2
Typically the easiest way is to graph and look for the function crossing the x axis.
+graph%28+300%2C+300%2C+-20%2C+20%0D%0A%2C+-10%2C+10%2C+x%5E3-4x%5E2%2B7x-2%29+
Looks like it crosses once at about x=1/3.
Since there are three roots for a cubic equation, the other two roots are complex.
Using Excel to window down the real solution gives x=0.349370808.
That gives a value of f(x)=-2.6e-9. That's pretty close to zero.
The other two roots are complex.
x=1.82531+%2B-+1.5468689i
There is an explanation of how to find zeros for a cubic equation at http://www.1728.com/cubic.htm.
+graph%28+300%2C+300%2C+-1%2C+2%0D%0A%2C+-10%2C+10%2C+x%5E3-4x%5E2%2B7x-2%29+
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The other function is simpler.
f%28x%29=%284x-7%29%5E20
This equals zero when %284x-7%29=0
4x-7=0
x=7%2F4
There are 20 roots at x=7/4.
+graph%28+300%2C+300%2C+-2%2C+3%2C+-10%2C+10%2C+%284x-7%29%5E20%29+