(m)^(2)+4bx-(a^(2)-b^(2))=0

Solve the following quadratic equation for x:4x^(2)+4bx-(a^(2)-b^(2))=0

Find the roots of the following equation 4x^(2)+4bx-(a^(2)-b^(2))=0 by the method of completing the square.

Solve by factorization: 4x^(2)+4bx-(a^(2)-b^(2))=0

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: 4x^(2)+4bx-(a^(2)-b^(2))=0

Solve the quadratic equation 4x^2+4bx-(a^2-b^2)=0

If (1)/((a^(2)-bx)(b^(2)-ax))=(A)/(a^(2)-bx)+(B)/(b^(2)-bx) , then the value of A and B respectively would be _________.

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)) .

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))

det[[ Prove that: ,b,ax+bya,c,bx+cyax+by,bx+cy,0]]=(b^(2)-ac)(ax^(2)+2bxy+cy^(2))