If ( a+1) and ( b+1) are roots of the equation 3 x 2 – 8 x - 1 = 0 , find that quadratic equation whose roots are a and b.
Answers
Answered by
0
Answer:
Open_in_app
Let α,β be the roots of 3x
2
−4x+1=1
Thus, α+β=
a
−b
=
3
−(−4)
=
3
4
and αβ=
a
c
=
3
1
The roots are
β
α
2
and
α
β
2
.
β
α
2
+
α
β
2
=
αβ
α
3
+β
3
=
αβ
(α+β)
3
−3αβ(α+β)
=
3
1
(
3
4
)
3
−3(
3
1
)(
3
4
)
=
3
1
27
64
−
3
4
=
3
1
27
64−36
=
3
1
27
28
=
27
28
×
1
3
=
9
28
Therefore,
β
α
2
α
β
2
=
αβ
(αβ)
2
=αβ=
3
1
The required equation is
x
2
− (Sum of the roots) x+ Product of roots =0
⇒x
2
−
9
28
x+
3
1
=0
⇒9x
2
−28x+3=0
Similar questions