roots

The smallest positive root of the equation x^5 - 5x^4 - 10x^3 + 50x^2 + 9x - 45 = 0 lies in the range

The solution of the differential equation $\frac{d^3y}{dx^3} - 5.5 \frac{d^2y}{dx^2} + 9.5 \frac{dy}{dx} - 5 y = 0$ is expressed as $y = C_1e^{2.5 x} + C_2e^{\alpha x} + C_3e^{\bet...

Consider the polynomial f(x) = x 3 $$-$$ 6x 2 + 11x $$-$$ 6 on the domain S, given by 1 $$\le$$ x $$\le$$ 3. The first and second derivatives are f'(x) and f''(x). Consider the fol...

Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are