1) Find the roots of the polynomial equation. x^3-2x^2+10x+136=0 Do not find the actual roots
In order to find the roots of the polynomial equation x^3 - 2x^2 + 10x + 136 = 0, we can use the rational root theorem and synthetic division. This theorem states that if a rational number p/q is a root of a polynomial equation, then p is a factor of the constant term (136 in this case) and q is a factor of the leading coefficient (1 in this case).
The possible rational roots for this equation can be found by taking the factors of 136 and dividing them by the factors of 1. The factors of 136 are ±1, ±2, ±4, ±8, ±17, ±34, ±68, ±136, and the factors of 1 are ±1. So, the possible rational roots are ±1, ±2, ±4, ±8, ±17, ±34, ±68, and ±136.
To find the actual roots, we would need to test each of these possible rational roots using synthetic division, which can be a time-consuming process. Therefore, in this case, we are asked not to find the actual roots.