x^(2)-b^(2)-4ac+4c^(2)

Factorise: a^(2) - b^(2) - 4ac + 4c^(2)

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)

a^2-b^2-4ac+4c^2

Factorise : a^(2)-9b^(2)+4c^(2)-25d^(2)-4ac+30bd

Four steps to derive the quadratic formula are shown below . (I) x^(2)+(bx)/a=(-c)/a (II) (x+b/(2a))^(2)=(b^(2)-4ac)/(4a^(2)) (III) x =pm sqrt((b^(2)-4ac)/(4a^(2)))-b/(2a) (IV) x^(2)+(bx)/a +(b/(2a))^(2)=(-c)/a + (b/(2a))^(2) What is the correct order for these steps ?

if alpha , beta are root of ax^2+bx+c=0 then (1/alpha^2+1/beta^2)^2 (a) (b^(2)(b^(2)-4ac))/(c^(2)a^(2)) (b) (b^(2)(b^(2)-4ac))/(ca^(3)) (c) (b^(2)(b^(2)-4ac))/(a^(4)) (d) (b^(2)-2ac)^2/(c^(4))

If alpha and beta are the roots of the equation ax^(2)+bc+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If alpha and beta are the roots of the equation ax^(2)+bc+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is