Question

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if sin theta and cos theta are the zeros of the equation ax^2+bx+c =0 prove that a^2-b^2+2ac=0​

Answer 1

If sin theta and cos theta are roots of equation ax^2+bx+c=0 prove that a^2-b^2+2ac =0






Let me assume theta is a
Sina+cosa=-b/a
Sina*cosa=c/a
By applying (A+B)^2 formulae
By A is sina, B is cosa
(Sina+cosa)^2=sin^2a+cos^2a +2sinacosa

b^2/a^2=1+2ca

Thus by calculation we get
a^2-b^2+2ac=0

..hence proved..