Question

Determine the rational roots of 2x⁵ - 11x⁴ + 14x³ - 2x² - 12x⁹ = 0.

a) 3/2
b) 1/2
c) -9/2
d) -1/2

Answer 1

To find the rational roots of the given polynomial equation, we can use the Rational Root Theorem. The possible rational roots are -1/2, 1/2, -9/2, and 3/2.

Step-by-step explanation:

The equation 2x⁵ - 11x⁴ + 14x³ - 2x² - 12x⁹ = 0 is a polynomial equation of degree 9. To find the rational roots, we can make use of the Rational Root Theorem. According to the Rational Root Theorem, any rational root of the equation can be expressed as p/q, where p is a factor of the constant term (-12) and q is a factor of the leading coefficient (2).

In this case, the possible rational roots are:

1. -1/2
2. 1/2
3. -9/2
4. 3/2

Therefore, the correct answer is d) -1/2, b) 1/2, c) -9/2, and a) 3/2.