Question

find all the zeroes of x3-x2-4x+4 if one of its zero is -2

Answer 1

HI friend,
Maximum number of zeroes a polynomial can have is equal to degree of the polynomial.
So given polynomial is a polynomial with degree 3 so it will have a maximum of 3 zeroes.
x³-x²-4x+4=0
sum of roots(zeroes) of a polynomial of the form ax³+bx²+cx+d=0
is -b/a
so let -2,g,h be zeroes of polynomial x³-x²-4x+4=0 
Here a=1,b=-1,c=-4,d=4
so sum of zeroes
-2+g+h=1
g+h=3   ====== equation 1

Product of roots of polynomial of the form ax³+bx²+cx+d=0 is -d/a
-2(g)(h)=-4
gh=2 
h=2/g
now substituting h in equation 1
g+2/g=3
g²-3g+2=0
g²-g-2g+2=0
g(g-1)-2(g-1)=0
g=1or g=2
so zeroes of polynomial x³-x²-4x+4=0 are -2,1,2.

HOPE THIS HELPS....

Answer 2

Step-by-step explanation:

yeah that's only half of the answer