If alpha, beta be the roots of a quadratic equation then x^2 - x (sum of roots) + product of roots = 0. x^2 - x(alpha + beta) + alpha beta = 0
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Answer:
Correct option is
B
bx
2
+a(b−1)x+(b−1)
2
=0
roots are α&β
sum = α+β = -a
product = αβ = b
new roots are α−
β
1
,β−
α
1
sum of roots =
=α−
β
1
+β−
α
1
=α+β−(
α
1
+
β
1
)
=(α+β)−(
αβ
α+β
)
=−a+
b
a
=
b
a−ab
product of roots =
(α−
β
1
)∗(β−
α
1
)
=αβ−1−1+
αβ
1
=b+
b
1
−2
=
b
b
2
−2b+1
Equation:
x
2
-(sum of roots)x+product of roots=0
x
2
−(
b
a−ab
)x+
b
b
2
−2b+1
=0
bx
2
+a(b−1)x+(b−1)
2
=0
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