Bro and sister plz solve this maths
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""" ❤️ Answer ❤️ """
Since α and β are the roots of
ax 2
bx+
c=
0,
therefore
α+ β= −
a
b
,αβ=
a
c
The equation
ax 2
bx(x−1)+
c
(x−1)
2
=
0
can be written as
x 2
(b−2c)x+
c=
0
Sum of the roots of this equation is
S= −
a−b+c
b−2c
=
a−b+x
−b+2c
=
1−
a
b
+
a
c
−
a
b
+
a
2c
⇒ S=
1+α+β+αβ
α+β+2αβ
=
α+1
α
+
β+1
β
Product of the roots
=
a−b+c
c
⇒ P=
1−
a
b
+
a
c
a
c
⇒ P=
1+α+β+αβ
αβ
=
α+1
α
.
β+1
β
Thus,
ax 2
bx(x−1)+
c
(x−1)
2
=
0
has
α+1
α
,
β+1
β
as its two roots.
Answered by
3
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