SOLUTION: Hi, 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

Question 519317: Hi,
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.
However none appear on the graph. I am lost as to what to do next. Thanks for the help.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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.
..
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)
..
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.
..
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.
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