For what triplets of real numbers (a, b, c) with a + 0 the functionx51otherwise is differentiable for all real x?i(xx) = ax2+bx+c

For what triplets of real numbers (a,b,c) with a!=0 the function f(x)=[x,x<=1 and ax^(2)+bx+c otherwise is differentiable for all real x?

The number of values of the triplet (a,b,c) for which a cos 2x+b sin^(2)x+c=0 is satisfied by all real x, is

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0

If a,b,c are real numbers and Delta >0 then the roots of ax^(2)+bx+c=0 are

If a,b,c are positive real numbers, then the roots of the equation ax^(2) + bx + c =0

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

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 .