#### 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 :

a x^{2}− 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}= b

^{2}/ a

^{2}

sin

^{2}θ + cos

^{2}θ + 2 sin θ cos θ = b

^{2}/ a

^{2}

1 + 2 c/ a = b

^{2}a

^{2}

(a + 2 / a = b

^{2}/ a

^{2}

(a + 2 c)/ a = b

^{2}/a

^{2}

( a + 2 c ) = b

^{2}/a

a

^{2}+ 2 a c = b

^{2}

a

^{2}− b

^{2}+ 2 a c =0