If $$\alpha$$ and $$\beta$$ ($$\ne$$ 0) are the roots of the quadratic equation x² + $$\alpha$$x $$-$$ $$\beta$$ = 0, then the quadratic expression $$-$$x² + $$\alpha$$x + $$\beta$$, where x $$\in$$ R has

Let $$\alpha$$ and $$\beta$$ be real number and z be a complex number. If z² + $$\alpha$$z + $$\beta$$ = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that

The equation $$\left| {1 - x} \right| + {x^2} = 5$$ hs

Let $$[x]$$ denote the greatest integer function. What is the number of solutions of the equation $${x^2} - 4x + [x] = 0$$ in the interval [0, 2] ?