Question 64742: Could someone please help me!!
I really need help asap please!!!!
Find the horizontal and vertical asymptotes of the function f(x)=x^2+3x-2/x-4
Find all real and complex zeros of the polynominal p(x)=2x^5-x^4+x^3+19x^2-11x-10
Thanks for all your help!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the horizontal and vertical asymptotes of the function f(x)=x^2+3x-2/x-4
Horizontal asymptote:
Look at the coefficients of x^2 in the numerator and denominator; they are
1 in the numerator and 0 in the denominator.
The horizontal asymptote is 1/0 which is undefined.
Therefore there is no horizontal asymptote.
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Verical asymptote:
These occur when the denominator is zero:
x-4=0 when x=4
So you have a vertical asymptote at x=4
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Find all real and complex zeros of the polynominal p(x)=2x^5-x^4+x^3+19x^2-11x-10
Zero at x=-2 (I got this by graphing p(x) on a TI-83
Using synthetic division maybe we can find other zeroes:
-2)...2....-1....1....19....-11....10
......2....-5...11....-3....-5..|...0
These coefficients add up to zero so x=1 is a zero.
1)....2....-3....8.....5..|..0
-1/2).2....-4....10..|.0
Quotient is now 2x^2-4x+10
Use the quadratic formula to find complex zeroes:
x=[4+-sqrt(16-4*2*10)]/4
x=[-4+-sqrt(16-80)]/4
x=-1+2i; x=-1-2i
Zeroes are x=1, -1/2, -2, -1+2i, -1-2i
Cheers,
Stan H.
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