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=0Submitted on 8/3/2024 | Answered by Vandana Rana
Answer :
ax2
−
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