Prove the following, using properties of determinants `|[a+bx^2 , c+dx^2,p+qx^2],[ax^2+b,cx^2+d,px^2+q],[

Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(ax^2+b,cx^2+d,px^2+q),(u,v,w)|=(x^4-1){:|(b,d,q),(a,c,p),(u,v,w)|

Differentiate the following function with respect of x:(ax+b)/(px^(2)+qx+r)

Differentiate the following function with respect of x backslash:(ax^(2)+bx+c)/(px^(2)+qx+r)

Using properties of determinant, If f(x)= a + bx + cx^(2) , prove that |(a,b,c),(b,c,a),(c,a,b)|= -f(1)f(omega)f(omega^(2)), omega is a cube root of unity

Differentiate the following function with respect of x:(px^(2)+qx+r)/(ax+b)

Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1-x^2)|[a,c,p],[b,d,q],[u,v,w]|

Prove that /_\ |[a+bx, c+dx, p+qx],[-ax+b, cx+d, px+q],[u,v,w]|=(1-x^2) [[a,c,p],[b,d,q],[u,v,w]]

The ratio of the roots of the equation ax ^2 + bx +c=0 is same as the ratio of the roots of the equation px^2 + qx +r=0 . If D_1 and D_2 are the discrimination of ax ^2 + bx + c=0 and px^2 +qx +r =0 respectively , then D_1 :D_2 =