If `ax^2 + bx + c = 0` is satisfied by every real value of x, then

If f(x)=ax+b and the equation f(x)=f^(-1)(x) be satisfied by every real value of x, then

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

If the quadratic equation ax^(2)+bx+c=0 when a!=0,a,b,c varepsilon Z is satisfied for more than two value then this must be an identity that it will be satisfied for all values of x, that is a=b=c=0

The expression ax^(2)+2bx+c, where 'a' is non-zerr real number,has same sign as that of a' for every real value of x,then roots of quadratic equation ax^(2)+(b-c)x-2b-c-a-0 are: (a) real and equal (b) real and unequal (c) non-real having positive real part(d) non-real having negative real part

The expression ax^2+2bx+b has same sign as that of b for every real x, then the roots of equation bx^2+(b-c)x+b-c-a=0 are (A) real and equal (B) real and unequal (C) imaginary (D) none of these

35.The expression ax^(2)+2bx+b has same sign as that of b for every,real x ,then the roots of equation bx^(2)+(b-c)x+b-c-a=0 are

Let f(x)=ax^(2)+bx+a,b,c in R. If f(x) takes real values for real values of x and non- real values for non-real values of x ,then a=0 b.b=0 c.c=0 d.nothing can be said about a,b,c.