Let a, b and c be three real and distinct numbers and `a(b-c)x^2+b(c-a)x+c(a-b)=0` be an equation, then which of the following must be true?

If a, b and c be three distinct real number in G.P. and a + b + c = xb , then x cannot be

If a, b and c be three distinct real number in G.P. and a + b + c = xb , then x cannot be

a,b and c are distinct real numbers such that a:(b+c)=b:(c+a)

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c< 0 , then which of the following is true?

For all real number a, b and c such that a > b and c < 0. Which of the following inequalities must be true?

Let a,b and c be three real and distinct numbers.If the difference of the roots of the equation ax^(2)+bx-c=0 is 1, then roots of the equation ax^(2)-ax+c=0 are always (b!=0)

Let a,b and c be three real numbers,such that a+2b+4c0. Then the equation ax^(2)+bx+c=0

Let a,b,c , are non-zero real numbers such that (1)/(a),(1)/(b),(1)/(c ) are in arithmetic progression and a,b,-2c , are in geometric progression, then which of the following statements (s) is (are) must be true?