If x, a, b, c are real and `(x-a+b)^(2)+(x-b+c)^(2)=0`, then a, b, c are in

If a, b, c are real then (b-x)^(2)-4(a-x) (c-x)=0 will have always roots which are

If a, b, c are real then (b-x)^(2)-4(a-x) (c-x)=0 will have always roots which are

If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b, then (a) a =-b=-c (c) a = b = c or a =-2b-_ 2c (b) a = 2b = 2c (d) none of these

If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b, then (a) a =-b=-c (c) a = b = c or a =-2b-_ 2c (b) a = 2b = 2c (d) none of these

If a , b , c , are real number such that a c!=0, then show that at least one of the equations a x^2+b x+c=0 and -a x^2+b x+c=0 has real roots.

If a, b, c are real and a!=b , then the roots of the equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

If a,b,c,x are all real numbers,and (a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0 prove that a,b,c are in G.P.,and x is their common ratio.

if the roots of (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal then a,b,c are in