If `a+b+c=0(a,b, c` are real), then prove that equation `(b-x)^2-4(a-x)(c-x)=0` has real roots and the roots will not be equal unless `a=b=c`.

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

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

Show that the roots of (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are real, and that they cannot be equal unless a=b=c.

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = 0 has no real roots then

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c) (x -a) =0 are always real and these cannot be equal unless a=b=c