Find all zeros of the given polynomial function
f(x)=2x^4-9x^3+2x^2+21x-10

Question

Find all zeros of the given polynomial function 
f(x)=2x^4-9x^3+2x^2+21x-10

diamondboy · Answer

its quiet long u knw?

anonymous · Answer

what?

anonymous · Answer

Do you know about rational zeros/roots theorem?

anonymous · Answer

I'm not familiar with it

campbell_st · Answer

the rational root theorem says find the factors of -10 and call them q

then find the factors of the leading term   2   and call them p

then the rational roots will be q/p

but so using this its   $$q = \pm 1, \pm 2 \pm 5, \pm 10$$

and 

$$p = \pm 1, \pm 2$$

just doing some mental arithmetic 

x = 2 is a zero you can check it by finding P(2)

so if x = 2 is a zero, (x - 2) is a factor

so you could do some polynomial division or some synthetic division

campbell_st · Answer

oops yu need to check by finding f(2) not P(2) sorry about that

anonymous · Answer

oh okay i'll try that thanks so much