SOLUTION: Show that the given values of c are zeros of P(x), and find all other zeros of P(x). P(x) = 4x4 − x3 − 28x2 − 17x + 6, c = 1/4, −2 x= ? (smallest value

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Show that the given values of c are zeros of P(x), and find all other zeros of P(x). P(x) = 4x4 − x3 − 28x2 − 17x + 6, c = 1/4, −2 x= ? (smallest value      Log On


   



Question 796422: Show that the given values of c are zeros of P(x), and find all other zeros of P(x).
P(x) = 4x4 − x3 − 28x2 − 17x + 6, c = 1/4, −2
x= ? (smallest value)
x= ? (largest value)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given: P%28x%29+=+4x%5E4+-x%5E3+-28x%5E2+-+17x+%2B+6, c+=+1%2F4, c=-2

0=4x%5E4+-x%5E3-28x%5E2+-17x+%2B+6
...
c+=+1%2F4
4c+=+1
4c+-+1+=+0 => %284x-1%29
...c+=+-2
c+%2B+2+=+0 => %28x%2B2%29
...
%284x-1%29%28x%2B2%29
From the given zeros we know
4x%5E2%2B7x-2
...
To find the remaining factors, divide
%284x%5E4+-x%5E3+-28x%5E2+-17x+%2B+6%29%2F%284x%5E2%2B7x-2%29=0........factor both numerator and denominator
...
%28%284+x-1%29+%28x%2B1%29+%28x%2B2%29+%28x-3%29%29%2F%28%284x-1%29%28x%2B2%29%29=0......simplify

+%28x%2B1%29+%28x-3%29=0
All four zeros:
1%2F4, -+2 : given
3, -1 : solved
so,
x=+-2 (smallest value)
x=3 (largest value)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E4+-x%5E3+-28x%5E2-17x+%2B+6%29+