Polynomials Tes...

the values of a& b so that the polynomial $${ x }^{ 3 }-{ ax }^{ 2 }-13x+b\quad is\quad divisible\quad by\quad \left( x-1 \right) \& \left( x+3 \right) $$ are 

Find the sum of all possible values of $$C$$ for which the expression $${x^3} + 3{x^2} - 9x + c$$ can be expressed as the product of three factors, two of which are identical and monic.

The real number 'K' for which teh equation $${\text{2}}{{\text{x}}^3} + 3x + K = 0$$ has to distinct real roots in [0, 1]

If two roots of the equation $$ x ^ { 3 } - 3 x + 2 = 0 $$ are same, then the roots will be

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

If $$x^5-5qx+4r$$ is divisible by $$(x-c)^2$$ then which of the following must hold true $$\forall q,r,c \in R?$$

The quadratic polynomials $$f(x) = ax^2 + bx + c $$ has real zeroes $$\alpha$$ and $$\beta$$ . If $$a$$ , $$b$$ , $$c$$ are real and of the same sign then 

If $$\alpha ,\beta ,\gamma$$ are zeroes of the polynomial $${ x }^{ 3 }-x-1$$, then the value of $$\frac { 1+\alpha  }{ 1-\alpha  } +\frac { 1+\beta  }{ 1-\beta  } +\frac { 1+\gamma  }{ 1-\gamma  }$$ is?

Which of the following is a perfect cube?

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