MATH SOLVE

3 months ago

Q:
# According to the rational root theorem, the following are potential roots of f(x) = 60x^2 - 57x - 18. Which is an actual root A) -6/5B) -1/4C) 3D) 6

Accepted Solution

A:

I would immediately use synthetic division to check the four possible answers.

Is -1/4 an actual root? Let's find out:

_____________________

-1/4 / 60 -57 - 18

-15 18

----------------------------

60 -72 0

Since there is no remainder, -1/4 IS a factor of the given polynomial, and the other factor can be found from the coefficients 60 - 72:

72

60x - 72 = 0 => x = ---- = 6/5

60

Is -1/4 an actual root? Let's find out:

_____________________

-1/4 / 60 -57 - 18

-15 18

----------------------------

60 -72 0

Since there is no remainder, -1/4 IS a factor of the given polynomial, and the other factor can be found from the coefficients 60 - 72:

72

60x - 72 = 0 => x = ---- = 6/5

60