What is a quartic function with only the two real zeros given?

x = -4 and x = -1
A. y = x^4 + 5x^3 + 5x^2 + 5x + 4
B. y = x^4 - 5x^3 - 5x^2 - 5x - 4
C. y = -x^4 + 5x^3 + 5x^2 + 5x + 4
D. y = x^4 + 5x^3 + 5x^2 + 5x - 5

Question

What is a quartic function with only the two real zeros given?

x = -4 and x = -1
	A. y = x^4 + 5x^3 + 5x^2 + 5x + 4 	
	B. y = x^4 - 5x^3 - 5x^2 - 5x - 4 	
	C. y = -x^4 + 5x^3 + 5x^2 + 5x + 4 	
	D. y = x^4 + 5x^3 + 5x^2 + 5x - 5

hartnn · Answer

just substitute your both x and find which one gives 0 for both

anonymous · Answer

I dont get it. Im just confusing myself.

anonymous · Answer

but how will you know the OTHER two zeros are REAL or complex?

hartnn · Answer

because only for one equation these two are zeros,for other 3 even these are not zeros

anonymous · Answer

@hartnn  it says with ONLY the two. Some of these can have more than 2 real roots. The systematic way i'd go around doing this would to

1) first substitute x =-4 and x=-1into the equations to see which ones actually have roots of -4 and -1(aka y=0)

anonymous · Answer

i'm with @dpalnc . You should carry out a systematic way to solve these

hartnn · Answer

i did that only and found out that only one equation has y=0......

anonymous · Answer

so you did do a systematic way....:)

hartnn · Answer

what i did was testing of options :P

hartnn · Answer

lets ask whether asker understood....Emily?

anonymous · Answer

nothing wrong with doing it by elimination... just becareful...:)

anonymous · Answer

hartnn, all i'm saying is what would you have done if there was two with roots -4 and -1

hartnn · Answer

will try to factorize...

hartnn · Answer

more specifically,first i will divide that by x+1 and x+4....because they are factors....and get the quadratic expression,which would be easier to solve for....

anonymous · Answer

could use descartes rule also =]

hartnn · Answer

i don't know what that is..

anonymous · Answer

http://www.purplemath.com/modules/drofsign.htm

anonymous · Answer

i didn't know it either until a few weeks ago lol

hartnn · Answer

doesn't give exact no of roots...

anonymous · Answer

So.. Whats the answer?

hartnn · Answer

its A :P

anonymous · Answer

Thanks!

anonymous · Answer

yes but it tells you the possible amount of negative roots .. if you get 2 posible negative roots. and you have 2 negative roots it means that there is only 2 non complex roots. if you look there is 0 possible roots due to no switching in signs

anonymous · Answer

0 possible positive roots