Question

Find integral roots of polynomial x3 -6x2+11x-6 explain briefly

Answer 1

Answer:
The zeros are
1
,
4
and
−
3
Explanation:
Given:
x
3
−
2
x
2
−
11
x
+
12
Sum of coefficients shortcut
Note that the sum of the coefficients is
0
. That is:
1
−
2
−
11
+
12
=
0
Hence,
x
=
1
is a zero and
(
x
−
1
)
a factor:
x
3
−
2
x
2
−
11
x
+
12
=
(
x
−
1
)
(
x
2
−
x
−
12
)

Answer 2

e zeros are 1, 4 and −3

Explanation:

Given:

x3−2x2−11x+12

Sum of coefficients shortcut

Note that the sum of the coefficients is 0. That is:

1−2−11+12=0

Hence, x=1 is a zero and (x−1) a factor:

x3−2x2−11x+12=(x−1)(x2−x−12)