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 RanaAnswer :
a x2 − b x + c = 0sin 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