Find all the real zeros of the polynomial

Question

find all the real zeros of the polynomial

P(x)=x⁴+x³-13x²-x+12

its real zeros are

x1=

x2=

x3=

x4=

with x1≤x2≤x3≤x4

Answer 1

Since P(1)=0 and P(-1)=0, thus (x-1) and (x+1) are factors of P(x).

Therefore (x-1)(x+1)=(x²-1) is also a factor of P(x).

 

using long division,

P(x)=(x²-6x+5)(x²-1)

= (x-1)(x+1)(x-5)(x+1)

 

Thus the zeros of P are

x1=-1

x2=-1

x3=1 and

x4=5.

 

Sorry. I don't have a computer with me now and could only reply via smart phone. This the presentation is limited.

let me know if you need clearer explanation on how to find the first two factors and how to do long division.