a^(2)x^(2)-3abac+2b^(2)=0

Solve by factorization: a^2x^2-3a b x+2b^2=0

Find the roots of the equation a^2x^2-3a b x+2b^2=0 by the method of completing the square.

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0

Solve for x 2a ^(2) x ^(2) + b( 6a ^(2) +1) x + 3b ^(2) =0

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 in x are equal, show that either a=0 or a^(3)+b^(3)+c^(3)=3abc .

If c^(2) != ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)+0 are equal show that a^(3)+b^(3)+c^(3)=3abc (or) a = 0.