Question 519317
The question states "Find all rational zeros of f. Then (if necessary) use the depressed equation to find all roots of the equations f(x)=0. 
3x^4-20x^3-20^x2-28x-7 
My possible zeros are +/- 1, 1/3, 7/3, 7.
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Rational Roots Theorem:
Synthetic Division
...0...|....3......-20.......-20.......-28......-7.
...1...|....3......-17.......-37.......-65......-72
...2...|....3......-14.......-48.......-124....-131
...3...|....3..............................................
...4...|....3..............................................
...5...|....3..............................................
...6...|....3......-2.........-32......-220.....-1327
...7...|....3........1.........-14......-126......-889 (sign switch on last number and all numbers>0)
...8...|....3........4.......... 12.........68.........537 (8 is upper bound, and (7 < x < 8)
...............................................................
...0...|....3......-20.......-20.......-28......-7.  (sign switch on last number and all numbers alternate in sign)
..-1..|....3......-23........3..........-31.......24 (-1 is lower bound, and (-1 < x < 0)
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According to the Rational Roots Theorem as shown above, one real root is between 7 & 8, and the other real root is between -1 and 0. The other two roots should be non-real or imaginary.
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According to my graphics computer program, the two roots are irrational: 7.69567 and -0.242438.
I don't no how to obtain these roots algebraically.