Polynomials Tes...

The zeroes of an expression represented by the

following graph are:

The zero polynomial has :

If $$\alpha, \beta$$ are real and $$\alpha^2, -\beta^2$$ are the roots of $$a^2 x^2 + x+1-a^2=0;\ (a  >  1)$$, then $$\beta^2=$$

If the zeros of the polynomial $$f(x)=k^2x^2-17x+k+2, (k > 0)$$ are reciprocal of each other, then the value of $$k$$ is

If the roots of $$x^2 - bx + c = 0$$ are each decreased by $$2$$, then resulting equation is $$x^2 - 2x + 1 = 0$$, if and only if

If the roots of the given equation $$2x^2+3(\lambda -2)x+\lambda +4=0$$ be equal in magnitude but opposite in sign, then value of $$\lambda$$ is

If $$\alpha, \beta, \gamma $$ are the roots of the equation $$2x^3-3x^2+6x+1=0$$, then $$\alpha^2 +\beta^2+ \gamma^2$$ is equal to

If $$'k'$$ be the ratio of the roots of the equation $$x^{2} - px +q = 0$$, the value of $$\dfrac{k}{1 + k^{2}}$$ is

If $$\alpha, \beta$$ be the zeros of the quadratic polynomial $$2x^2+5x+1$$, then the value of $$\alpha+\beta+\alpha \beta=$$

Quadratic polynomial having sum of it's zeros is 5 and product of it's zeros is - 14 is