Polynomials Tes...

Write the correct alternative answer for the following question .
Which of the following is a polynomial .

Find all the zeros of the polynomial $$x^4-3x^3-10x^2+36x-24$$, if $$\sqrt{12}$$ and $$-\sqrt{12}$$ are two of its zeros.

Find the sum of zeroes of the polynomial $$2x^4+x^3-14x^2-19x-6$$, if two of its zeroes are $$-1$$ and $$3$$

If the two zeros of the polynomial  $${ x }^{ 2 }-85x+c=0$$ are prime numbers, what is the value of the sum of the digits of c?

Consider the cubic equation $${x^3} - \left( {1 + \cos \theta  + \sin \theta } \right){x^2} + \left( {\cos \theta \sin \theta  + \cos \theta  + \sin \theta } \right)x - \sin \theta \cos gq = 0,$$ whose roots are $${x_1},{x_2}\,\,{\text{and}}\,\,{x_3}.$$ 
1. The value of $$x_1^2 + x_2^2 + x_3^2$$ equals

If $$\alpha,beta$$ are zeros of polynomial $$f(x)=2x^2+5x+k$$ satisfying the relation $$\alpha^2+\beta^2+\alpha\beta=\cfrac{21}{4}$$ then K=

State whether the given algebraic expressions are polynomials ?

If $$\alpha$$,$$\beta$$ are zero of quadratic polynomial $$\displaystyle kx^2 + 6x + 6 $$, then find the value of k such that $$ \displaystyle ( \alpha + \beta )^2 2\alpha \beta = 24 $$

If the zeroes of the polynomial f(x) =$${ x }^{ 3 }-{ 9kx }^{ 2 }+52kx-24{ k }^{ 3 }$$ are in the ratio 2:3:4, then the possible value of k is 

If $$\alpha $$ and $$\beta $$ are zeros of the quadratic polynomial $$f(x)=ax^2+bx+c$$, then $$\frac {\beta}{a\alpha +b}+\frac {\alpha }{a\beta +b}=$$