Let `sinx` and `siny` be roots of the quadratic equation `asin^2theta+bsintheta+c=0` such that `sinx+2siny=1` , then the value of `(a^2+2b^2+3ab+ac)` equals

If sin theta and cos theta are the roots of the quadratic equation ax ^(2) +bx + c=0(a ne 0). Then find the value of (b ^(2) -a^(2))/(ac ).

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 be equal to the sum of their squares, then prove that 2ac=ab+b^(2) .

If both the distinct roots of the equation |sinx|^(2)+|sinx|+b=0 in [0,pi] are real, then the values of b are

If alpha and beta are roots of the equation acostheta+bsintheta=c then prove that, sin(alpha+beta)=(2ab)/(a^(2)+b^(2))

If sinx+cosy=(1)/(3) and cos x+siny=(3)/(4) , then the value of tan((x-y)/(2)) is equal to

a +b , b+ c 1- ab 1- bc o b, are in For a, b, CER1O), let AP. If ?, ? are the roots of the quadratic equation 2acx2 + 2abcx + (a + c) 0, then the value of 1 + ?)(1 + ?) is

If the solution of the differential equation (dy)/(dx)=1/(xcosy+sin2y) is x=c e^(siny)-k(1+siny), then the value of k is_______

If the solution of the differential equation (dy)/(dx)=1/(xcosy+sin2y) is x=c e^(siny)-k(1+siny), then the value of k is_______