If `tanthetaa n dsectheta` are the roots of `a x^2+b x+c=0,` then prove that `a^4=b^2(b^2-4ac)dot`

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

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 and alpha+delta,beta+delta are the roots of the equation Ax^(2)+Bx+C=0 then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2)) for some constant value of delta

If a,b,c are in AP,then prove that (a-c)^(2)=4(b^(2)-ac)

Let alpha and beta be the roots of the equationa x^(2)+2bx+c=0 and alpha+gamma and beta+gamma be the roots of Ax^(2)+2Bx+C=0. Then prove that A^(2)(b^(2)-4ac)=a^(2)(B^(2)-4AC)

If 'alpha and beta are roots of ax^(2)+bx+c=0 ,and roots differ by k then b^(2)-4ac=

If alpha and beta are roots of ax^(2)+bx+c=0 ,and roots differ by k then b^(2)-4ac=

The roots of ax^(2)+bx+c=0, ane0 are real and unequal, if (b^(2)-4ac)

If the roots of the equation ax^2+bx+c=0 differ by K then b^(2)-4ac=

If alpha,beta are the roots of ax^(2)+bx+c=0,(a!=0) and alpha+delta,beta+delta are the roots of Ax^(2)+Bx+C=0,(A!=0) for some constant delta then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2))

If alpha , beta are the roots of ax^(2) +bx+c=0, ( a ne 0) and alpha + delta , beta + delta are the roots of Ax^(2) +Bx+C=0,(A ne 0) for some constant delta , then prove that (b^(2)-4ac)/(a^(2))=(B^(2)-4AC)/(A^(2)) .