If `s intheta,costheta` be the roots of `a x^2+b x+c=0` , then prove that `b^2=a^2+2a cdot`

If sinthetaand costheta are the roots of the equation ax^2-bx+c=0 , show that : a^2+2ac-b^2=0 .

If sintheta and costheta are roots of the equation ax^(2)+bx+c=0 , prove that a^(2)-b^(2)+2ac=0 .

If sinthetaand costheta are the roots of the equation ax^2+bx+c=0 , then (A) (a-c)^2=b^2+c^2 (B) (a+c)^2=b^2-c^2 (C) a^2=b^2-2ac (D) a^2+b^2-2ac=0

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

If the ratio of the roots of the equation x^(2)+px+q=0 are equal to ratio of the roots of the equation x^(2)+bx+c=0, then prove that p^(2c)=b^(2)q

If beta+cos^(2)alpha,beta+sin^(2)alpha are roots of x^(2)+2bx+c=0 and gamma+cos^(4)alpha,gamma+sin^(4)alpha are the roots of X^(2)+2BX+C=0 then prove that b^(2)-B^(2)=c-C

If alpha,beta are the nonzero roots of ax^(2)+bx+c=0 and alpha^(2),beta^(2) are the roots of a^(2)x^(2)+b^(2)x^(2)+b^(2)x+c^(2)=0, then a,b,c are in a.G.P.b.H.P. C.A.P.d.none of these

If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

If the centroid of a triangle formed by the points (0,0), (costheta,\ s intheta)a n d\ (s intheta,\ -costheta) lies on the line y=2x then write the value of t a nthetadot