Answer to Question #181169 in Algebra for will

Question

Based on the Rational Root Theorem, which of the following is not possible roots of the function:

2x²- 9x²+ 13x - 6

a. -3/2

b. 6

c. 1/2

d. -9

Answer 1

Given, the function 2x²-9x²+13x-6.

Simplify the equation,

-7x²+13x-6

In rational root theorem,

a_nxⁿ+a_n-1x^n-1+...+a₀x+a=0 is the equation.

Where a_n, a_n-1, ..., a are integers.

The above general equation have a rational solution p/q, where q must divide a_n and p must divide a₀.

Therefore, by rational root theorem,

Then the divisors of 6 are 1, 2, 3 and 6, and the divisors of 7 are 1 and 7.

Thus, if any rational roots exist, they must have a denominator of 1 or 7 and a numerator of 1, 2, 3, or 6, which limits the choices to 1/7, 2/7, 3/7, 6/7 , 1, 2, 3, and 6 and their corresponding negative values.

Therefore, option a, c and d are not possible root of the given function.