if zeroes of the polynomial f(x)=x^3-3x^2-6x+8 are of the form a-b ,a,a+b find a and b
Answers
Answered by
1
Answer:
a
=
−
1
and
b
=
±
√
2
Explanation:
As coefficient of highest power
x
3
is
1
, if three roots are
α
,
β
and
γ
, we have
x
3
−
3
x
2
+
x
+
1
=
(
x
−
α
)
(
x
−
β
)
(
x
−
γ
)
=
x
3
−
(
α
+
β
+
γ
)
x
2
+
(
α
β
+
β
γ
+
γ
α
)
x
+
α
β
γ
Now let us compare coefficients of similar powers on each side. First comparing sum of roots from coefficient of
x
2
, we have
a
−
b
+
a
+
a
+
b
=
−
3
i.e.
3
a
=
−
3
i.e.
a
=
−
1
.
Also coefficients of
x
give us
a
(
a
−
b
)
+
a
(
a
+
b
)
+
(
a
+
b
)
(
a
−
b
)
=
1
i.e.
a
(
a
−
b
+
a
+
b
)
+
a
2
−
b
2
=
1
or
3
a
2
−
b
2
=
1
and as
a
=
−
1
,
b
2
=
3
×
(
−
1
)
2
−
1
=
2
and
b
=
±
√
2
Further, products of roots is
(
a
−
b
)
a
(
a
+
b
)
=
1
.
and as
a
(
a
2
−
b
2
)
=
(
−
1
)
(
1
−
2
)
=
1
, this is true as
α
β
γ
=
1
Hence,
a
=
−
1
and
b
=
±
√
2
Answered by
1
a= 3 & 1
b= -1 & 1
I HOPE YOU WILL UNDERSTAND
b= -1 & 1
I HOPE YOU WILL UNDERSTAND
anshkumar6228ped4df:
thanks a lot
Similar questions