Question :

If sin θ and cos θ are the roots of the equation a x ²− b x + c = 0 , then prove that a²-b²+2ac=0
Submitted on 8/3/2024 | Answered by Vandana Rana

Answer :

a
x2


b
x
+
c
=
0


sin
θ
and
cos
θ
are roots.


sin
θ
+
cos
θ
=
b/
a (sum of zeroes)

;
sin
θ

cos
θ
=
c/
a (product of zeroes)


Then
(
sin
θ
+
cos
θ
)2
=
b2/

a2




sin
2
θ
+
cos2

θ
+
2
sin
θ
cos
θ
=
b2/

a2




1
+
2
c/
a
=
b2

a2




(a
+
2
/
a
=
b2/

a2




(a
+
2
c)/
a

=
b2/a2



(
a
+
2
c
)

=
b2/a




a2

+
2
a
c
=
b2




a2


b2

+
2
a
c
=0