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