SOLUTION: I am having problem with two questions Divide the following: 6x - 5 divide bar 30x4 - x3 - 38x2 + 3x + 13 Find ALL real roots of f(x): f(x)=4x^4-13x^3-13x^2+52x-12

Question 547935: I am having problem with two questions
Divide the following:
6x - 5 divide bar 30x4 - x3 - 38x2 + 3x + 13

Find ALL real roots of f(x):
f(x)=4x^4-13x^3-13x^2+52x-12

thanks sooooo much
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find ALL real roots of f(x):
f(x)=4x^4-13x^3-13x^2+52x-12
**
Using Rational Roots Theorem to solve:
...0...|.....4.......-13.....-13.......52.......-12
...1...|.....4.......-9.......-22.......30.........18 (There is a root between 0 and 1)
...2...|.....4.......-5.......-23.......6............0 (2 is a root)
=========================
...0...|.....4.......-5.......-23.......6
...3...|.....4.........7.......-2.........0 (3 is a root)
...4...|.....4.......-5.......-23.......6
...5...|.....4.......15........52.......260 (5 is upper limit, no change in signs)
====================
...0...|.....4.........7.......-2
.-1...|.....4.........3.......-5
.-2...|.....4.......-1....... 0 (-2 is a root)(also, lower limit, alternate signs)
f(x)=(x-2)(x-3)(x+2)(4x-1)
ans:
Real Roots: -2, 1/4, 2, and 3
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