Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems.
P(x)= 2x^4+x^3-20x^2-13x+30
2007-10-26 06:18:00 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Well, you can see that 1 is a zero of P(x)
since 2 + 1 -20-13+30 = 0, so x -1 is a factor.
So if we divide synthetically by x-1 we get
2x³ +3x²-17x-30. (*)
Now let's use the rational roots theorem.
Let a/b be a zero of (*). Then a divides 30 and
b divides 2. If we try some possibilities, we see 3 is
a zero of (*). So (x-3) is a factor. The quotient is
2x²+9x+10.
To find the zeros of this, factor it:
2x²+9x+10 = 0
(2x+5)(x+2) = 0
x = -2 and x = -5/2.
So the zeros of P(x) are -5/2, -2, 1 and 3.
2007-10-26 06:33:42 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
This is a very lengthy discussion. TYhe shortcut would be to graph the function on the calculator and find the zeros. This would not help find the irrational zeros but you could use the answers you do get to complete the problem.
2007-10-26 06:28:07 · answer #2 · answered by roguetrader12002 4 · 0⤊ 0⤋