Isolating the real roots of a polynomial

Determine the number of real roots of the following equation, and locate the intervals containing these roots:

Determine the number of real roots of the following equation, and locate the intervals containing these roots:

Determine the number of real roots of the following equation, and locate the intervals containing these roots:

Determine the number of real roots of the following equation, and locate the intervals containing these roots:

Isolate the real roots of the equation $x^{3}-12x+5=0$.

Isolate the real roots of the equation $x^{3}-27x-17=0$.

Isolate the real roots of the equation $x^{4}-2x^{3}-5x^{2}+2x+2=0$.

Isolate the real roots of the equation $x^{4}-2x^{3}-5x^{2}+3x+1=0$.

Isolate the real roots of the equation $x^{5}-2x^{4}-5x^{3}+19x^{2}-17x+1=0$.

Isolate the real roots of the equation $x^{5}+3x^{4}-9x^{3}-7x^{2}+39x-21=0$.

Isolate the roots of the equation, with respect to $\lambda$:

Prove that all the roots of the derivative of the polynomial

are real, and find their isolation intervals of length at most 0.5.

Prove that the polynomial:

Prove that the equation $x^{5}+x^{4}+x^{2}+10 x-5 = 0$ has a unique root, and indicate its isolation interval of length not exceeding 0.1.

Separate the real roots of the equation, indicating isolation intervals of length not exceeding unity:

Separate the roots of the equation $\frac{p^{2}}{a^{2}+x}+\frac{q^{2}}{b^{2}+x}+\frac{r^{2}}{c^{2}+x} = 1$, where $p, q, r, a, b, c \in \mathbb {R}, a^{2} > b^{2} > c^{2}, \quad p q r \neq 0$.