Q36 Roots of equation X^3
+2X^2 - 5X-6=0 is
Answers
Answered by
5
Step-by-step explanation:
If we note that the sum of the coefficients of the terms equals zero
then it follows that
x
=
1
is one solution to this equation.
That is
(
x
−
1
)
is a factor of the right side.
Either using synthetic or long division we can obtain
XXX
(
x
3
−
2
x
2
−
5
x
+
6
)
÷
(
x
−
1
)
=
x
2
−
x
−
6
Using basic principles we can factor
XXX
(
x
2
−
x
−
6
)
=
(
x
−
3
)
(
x
+
2
)
So
x
3
−
2
x
2
−
5
x
+
6
=
0
→
(
x
−
1
)
(
x
−
3
)
(
+
2
)
=
0
giving the solutions
XXX
x
=
+
1
or
x
=
+
3
or
x
=
−
2
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