Question 1 :
Suppose $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $ then $f(x)=$
Question 2 :
If $\cos{\cfrac{\pi}{7}},\cos{\cfrac{3\pi}{7}},\cos{\cfrac{5\pi}{7}}$ are the roots of the equation $8{x}^{3}-4{x}^{2}-4x+1=0$<br>The value of $\sec{\cfrac{\pi}{7}}+\sec{\cfrac{3\pi}{7}}+\sec{\cfrac{5\pi}{7}}=$
Question 3 :
If roots of cubic equation are in G.P. , $ ax^3 + bx^2 + cx + d $ then :<br/>
Question 4 :
If $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }-5x+4=0$ then ${ \left( { \alpha }^{ 3 }+{ \beta }^{ 3 }+{ \gamma }^{ 3 } \right) }^{ 2 }=$
Question 5 :
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2 - (\sqrt{5} -1)x -(\sqrt{5} + 1)$, then the value of $\displaystyle \frac{1}{\alpha^2} + \frac{1}{\beta^2}$ is ____________.
Question 6 :
The number of integers $n$ for which $3x^3-25x+n=0$ has three real roots is$?$<br/>
Question 7 :
Given $l{x^2} - mx + 5 = 0$ does not have distinct real roots then minimum value of $5l+m$ is
Question 8 :
The number of different possible values for the sum $x+y+z$, where $x,y,z$ are real numbers such that ${x}^{4}+4{y}^{4}+16{z}^{4}+64=32xyz$ is
Question 9 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to
Question 10 :
Number of intergers in the range of 'a' so that the equation ${ x }^{ 3 }-3x+a=0$ has all its roots real and distinct,is