Polynomials Tes...

The roots of $$6x^{4}-35x^{3}+62^{2}-35x+6=0$$ are.......

If $$p,\quad q,\quad r,\quad s\quad \in R$$, then equation $$({ x }^{ 2 }+{ px }+{ 3 }q)({ -x }^{ 2 }+rx+q)({ -x }^{ 2 }+sx-2q)=0$$ has

If $$a,\beta ,y$$ are the roots of equation $${ x }^{ 3 }+2x-5=0$$ and if equation $${ x }^{ 3 }+{ bx }^{ 2 }+cx+d=0\quad has\quad roots\quad 2a+1.\quad 2\beta +1,\quad 2y+1.$$ then value of $$\left| b+c+d \right| $$ is (where b,c,dd are coprime ) -

Let $$f ( x )$$ be a polynomial of degree 5 with leading coefficient unity, such that $$f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2$$ and $$f ( 5 ) = 1 ,$$ then 
Sum of the roots of $$f ( x )$$ is equal to:

Let for $$a \neq a_1 \neq 0, f(x) = ax^2 +bx +c, g(x) = a_1x^2 +b_1x+c_1$$ and $$p(x) =f(x) -g(x)$$. If $$p(x) =0$$ only for $$x- -1$$ and $$p(-2) =2$$ then the value of $$p(2)$$ is

Let $$f ( x )$$ be a polynomial of degree 5 with leading coefficient unity, such that $$f ( 1 ) = 5 , f ( 2 ) = 4 , f ( 3 ) = 3 , f ( 4 ) = 2$$ and $$f ( 5 ) = 1 ,$$ then 
Product of the roots of $$f ( x )$$ is equal to:

The expansion $$\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x - 1} }}{2}} \right]}^7}} \right]$$ is a polynomial in x of degree 

The expression $${ \left[ x+{ \left( { x }^{ 3 }-1 \right)  }^{ 1/2 } \right]  }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right)  }^{ 1/2 } \right]  }^{ 5 }$$ is a polynomial of degree

If a is a non-real root of $${ x }^{ 6 }=1$$, then $$\dfrac { { a }^{ 5 }{ a }^{ 3 }+a+1 }{ { a }^{ 2 }+1 } $$ is

The equation $${\left( {x - 3} \right)^9} + {\left( {x - {3^2}} \right)^9} + {\left( {x - {3^3}} \right)^9} + .... + {\left( {x - {3^9}} \right)^9} = 0\;has:$$