<p>ok i am dumb in math and i cannt figure these problems out.
First find all the real roots of x^6-4x^3+4=F(x)
Find all the rational roots of f(x)=x^4-2x^3-4x^2+1
Find all roots of f(x)=2x^3+3-8x^2+5x</p>
<p>This is from my review guide for my pre-cal test tommorrow, and we hve to do these by hand without the helping of the calulator and i spend the last hour trying to figure out what is going on...like we are suppose to do synetic division to find the first 0 but i dont know what do after that...</p>
<p>P.S- id be great if someone can clearify the difference between REAL and RATIONAL roots for me...</p>
<p>Mucho thanks....i really appericate this and i wil give you all imaginary hugs should i ace the test....:)</p>
<p>I don't remember too much from pre-calc. But I know to find the roots you take the coefficient (or last number) of the smallest term and you put the factors of that number over the factors of the coefficient of the largest term, and then you find all the possible +/- combinations (*Note: all of the fractions can be possitive or negative). Then you use synthetic division to see where you can get it to equal 0, and those values are roots.</p>
<p>I'm not quite sure...but I think real roots are real numbers (like whole numbers, fractions, positive/negative numbers). And rational roots might include i...I think.</p>
<p>Remember a=x^3. So,
x^3 = 2
x = cube root of 2.</p>
<p>For the second one, I couldn't figure it out. I'll let you know if I figure it out later.</p>
<p>Now the third, 2x^3 + 3 - 8x^2 + 5x
which is the same as 2x^3 -8x^2 + 5x +3
Possible rational zeros : 1, -1, 1/2, -1/2, 3/2, -3/2, 3, -3, 2, -2
When you do the synthetic division, 3 works.
Then, in the remainder you will be left with 2 -2 -1 and 0
This can be translated back into exponetial form 2x^2 - 2x -1
Use quadratic equation and you will get 2 +/- square root of 12 all over 4.<br>
So, final answers are the + and - roots from quadratic equation and 3. </p>
<p>Good luck on your test! Hope this helped!! = )</p>
<p>Rational: a real number that can be expressed as a fraction with integral numerator/denominator, like 58/7.
Real: anything that's not imaginary. Any number that has a place on the number line is real - including transcendental numbers like pi and algebraic-but-irrational numbers like sqrt(2).</p>
<p>Example: (x-i)(x-pi)(x^2-2)(x-3/2) has one rational root, four real roots, and five roots altogether.</p>
<p>Rational root theorem: any rational root of f(x) = c<em>nx^n+c</em>(n-1)x^(n-1)+...+c<em>1x + c</em>0 is of the form + or - a/b, where a is a factor of c<em>0 and b is a factor of c</em>n.</p>
<p>Thanks for all the help.
I got 80/100 on my test. Which isnt great but its an improvement over my other tests. I am having some trouble with this chapter. </p>