SOLUTION: Show that the given values of c are zeros of P(x), and find all other zeros of P(X) P(X)= 3x^4-x^3-21x^2-11x+6 c=(1/3), -2

Algebra ->  Equations -> SOLUTION: Show that the given values of c are zeros of P(x), and find all other zeros of P(X) P(X)= 3x^4-x^3-21x^2-11x+6 c=(1/3), -2      Log On


   



Question 675207: Show that the given values of c are zeros of P(x), and find all other zeros of P(X)
P(X)= 3x^4-x^3-21x^2-11x+6 c=(1/3), -2

Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
0 = 3x%5E4-x%5E3-21x%5E2-11x%2B6
...
c = 1/3
3c = 1
3c - 1 = 0
(3x-1)
...
c = -2
c + 2 = 0
(x+2)
...
(3x-1)(x+2)
3x%5E2+%2B+6x+-+x+-+2
From the given zeros we know
3x%5E2+%2B+5x+-+2
...
To find the remaining factors, divide
%283x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6%29%2F%283x%5E2%2B5x-2%29
...
3x%5E2+%2B+5x+-+2 goes into 3x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6 : x^2
to get
3x%5E4+%2B+5x%5E3+-+2x%5E2
subtracting
3x%5E4+-+3x%5E4+-+x%5E3+-+5x%5E3+-+21x%5E2+-+-2x%5E2
yielding
-6x%5E3+-+19x%5E2
...
3x%5E2%2B5x-2 goes into -6x%5E3-19x%5E2-11x : -2x
to get
-6x%5E3+-+10x%5E2+%2B+4x
subtracting
-6x%5E3+-+-6x%5E3+-+19x%5E2+-+-10x%5E2+-+11x+-+4x
yielding
-9x%5E2-15x
...
3x%5E2%2B5x-2 goes into -9x%5E2-15x%2B6 : -3
to get
-9x%5E2+-+15x+%2B+6
subtracting
-9x%5E2+-+-9x%5E2+-+15x+-+-15x+%2B+6+-+6
yielding
0
...
...
%283x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6%29%2F%283x%5E2%2B5x-2%29+=+x%5E2-2x-3
...
x%5E2-2x-3
(x-3)(x+1)
...
All for zeros
1%2F3, - 2 : given
3, -1 : solved
.....................
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