The roots of `(x-a)(x- b)=abx^2` (a) are always real (c) are real and equal if and only if `a= b` (b)may be complex depending upon a (d)are real and distinct if and only if `a!=0`

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

The roots of the equation a^(2)x^(2)+(a+b)x-b^(2)=0(a,b!=0) are :(A) real and different (B) real and equal (C) imaginary (D) None

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.

If a,b,c are distinct positive numbers,then the nature of roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=1/x is a.all real real and is distinct b.all real and at leat two are distinct c.at least two real d.all non-real

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1/(x-a) + 1/(x-b) + 1/(x-c) = 1/x is a) all real and is distinct b) all real and at least two are distinct c) at least two real d) all non-real

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

IF a,b,c are real, prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real and cannot be equal unless a=b=c.

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is Option a) all real and is distinct Option b) all real and at least two are distinct Option c) at least two real Option d) all non-real