Let a, b, c be non zero numbers such that
`int_(0)^(3)sqrt(x^(2)+x+1)(ax^(2)+bx+c)dx=int_(0)^(5)sqrt(1+x^(2)+x)(ax^(2)+bx+c)dx`. Then the quadratic equation `ax^(2)+bx+c=0` has

Let a,b,c be non-zero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx then the quadratic equation ax^(2)+bx+c=0 has -

Let a, b, c be non-zero real numbers such that ; int_0^1 (1 + cos^8 x)(ax^2 + bx + c)dx = int_0^2 (1+cos^8 x)(ax^2 + bx +c)dx then the quadratic equation ax^2 + bx + c = 0 has -

Let a,b,c be nonzero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx=0 Then show that the equation ax^(2)+bx+c=0 will have one root between 0and 1 and other root between 1 and 2.

Let a,b,c be non - zero real numbers such that int_(0)^(3)(3ax^(2)+2bx+c)dx=int_(1)^(3)(3ax^(2)+2bx+c)dx . Then

Let a, b and c be non - zero real numbers such that int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx , then

Let a, b and c be non - zero real numbers such that int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx , then

If a,b,c are non-zero real numbers such that int_(0)^(1) ( 1+ cos^(8) x) (ax^(2) + bx + c ) dx = int _(0)^(2) (1+cos^(8)x) (ax^(2) + bx + c ) dx = 0 ,then the equation ax^(2) + bx +c = 0 will have

If ax^(2)+bx+c=0 be a quadratic equation, then

int_(0)^(3)(3ax^(2)+2bx+c)dx=int_(1)^(3)(3ax^(2)+2bx+c)dx