If `sin theta, cos theta` are the roots of `ax^(2)+bx+c=0` then prove that `b^(2)=a^(2)+2ac`

If alpha, beta are the roots of ax^(2)+2bx+c=0 and alpha +delta, beta + delta are those of Ax^(2)+2Bx+C=0 , then prove that (b^(2)-ac)/(B^(2)-AC)= ((a)/(A))^(2)

If sin alpha and cos alpha are the roots of the equition ax^(2) + bx + c = 0 , then

If secthetaandtan theta are the roots of ax^(2)+bx+c=0,(a,bne0) , then the value of sectheta-tan theta is

If alpha, beta are the roots of the equation ax ^(2) + bx + c =0, then the value of (1)/( a alpha + b) + (1)/( a beta + b) equals to : a) (ac)/(b) b) 1 c) (ab)/(c) d) (b)/(ac)

If the ratio of the roots of ax^(2) +2bx+c=0 is same as the ratio of the px^(2)+2qx +r= 0 , then prove that (b^(2))/(ac)= (q^(2))/(pr)

If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .