If `x in R ,a n da ,b ,c` are in ascending or descending order of magnitude, show that `(x-a)(x-c)//(x-b)(w h e r ex!=b)` can assume any real value.

If x in R, and a,b,c are in ascending or descending order of magnittude,show that (x-a)(x-c)/(x-b) (where x!=b) can assume any real value.

For real values of x, the expression ((x - b) (x - c))/((x - a)) will assume all real values provided :

A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

A certain polynomial P(x)x in R when divided by k x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

A certain polynomial P(x)x in R when divided by k x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot