Polynomials Tes...

The roots of the equation $$ax^3 + bx^2 - x + 1=0$$ are real, distinct and are in H.P., then

The expression $$(x+(x^4-1)^{1/2})^4 + (x-(x^4-1)^{1/2})^4$$ is a polynomial of degree

The sum of the roots of the equation $$cot-1x-1(x+2)=150$$ is

If $$\alpha ,\beta ,\gamma $$ are roots of $$7{ x }^{ 3 }-x-2=0$$ then find the value of $$\sum { \left( \dfrac { \alpha  }{ \beta  } +\dfrac { \beta  }{ \alpha  }  \right)  } $$

If roots of equation $$8x^3 -14x^2+7x-1 =0$$ are in geometric progression, then roots are 

If $$1,-2,3$$ are the roots of $${ x }^{ 3 }-b{ x }^{ 2 }+ax+6=0$$, then a=

number of real roots of the equation
$$\sqrt { x } +\sqrt { x-\sqrt { 1-x }  } =1\quad is$$

The HCF of two ploynomials $$A$$ and $$B$$ using long division method was found to be $$2x + 1$$ after two steps . The fisrt two quotient obtained are $$x$$ and $$(x + 1)$$ . Find $$A$$ and $$B$$ . Given that degree of $$A$$ > degree of $$B$$ is 

The root of the equation $${ X }^{ 4 }-1=0$$ are;

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