SOLUTION: What is a quartic function with only the two real zeros given? x = -4 and x = -1 A. y = x4 + 5x3 + 5x2 + 5x + 4 B. y = x4 - 5x3 - 5x2 - 5x - 4 C. y = -x4 + 5x3 + 5x2

Algebra ->  Functions -> SOLUTION: What is a quartic function with only the two real zeros given? x = -4 and x = -1 A. y = x4 + 5x3 + 5x2 + 5x + 4 B. y = x4 - 5x3 - 5x2 - 5x - 4 C. y = -x4 + 5x3 + 5x2       Log On


   

Question 669024: What is a quartic function with only the two real zeros given?
x = -4 and x = -1
A. y = x4 + 5x3 + 5x2 + 5x + 4
B. y = x4 - 5x3 - 5x2 - 5x - 4
C. y = -x4 + 5x3 + 5x2 + 5x + 4
D. y = x4 + 5x3 + 5x2 + 5x - 5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
My solution mmay not be the expected way to go about it, but here it is.
The four answers feature four different quartic polynomials.
I'll call them:
A%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4
B%28x%29=+x%5E4+-+5x%5E3+-+5x%5E2+-+5x+-+4
C%28x%29=+-x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+%2B+4
D%28x%29=+x%5E4+%2B+5x%5E3+%2B+5x%5E2+%2B+5x+-+5
For x=-1, their values are:

B%28-1%29=+%28-1%29%5E4+-+5+%28-1%29%5E3+-+5+%28-1%29%5E2+-+5%28-1%29+-+4=1%2B5-5%2B5-4=2


Only a%28x%29+has+%7B%7B%7Bx=-1 for a zero.
Does it have x=-4 for a zero?
Does it have any other zeros?
You would expect it to have x=-4 for a zero, and to have no other real zeros.
I would chose answer A and be done.
However, I can answer those two questions by factoring the polynomial.


That is the complete factorization.
Because x%5E2%2B1=0 has no real solutions, teh only zeros are the values of x that make the other two factors zero.
x%2B1=0 <--> highlight%28x=-1%29 and x%2B4=0 <--> highlight%28x=-4%29