How do you find the roots, real and imaginary, of #y=12x^2 - 42x + 18 # using the quadratic formula?

1 Answer
Mar 22, 2016

Answer:

1/2 and 3

Explanation:

#y = 12x^2 - 42x + 18 = 0.#
Use the improved quadratic formula (Google, Yahoo Search)
#D = d^2 = b^2 - 4ac = 1764 - 864 = 900# --> #d = +- 30#
There are 2 real roots:
#x = -b/(2a) +- d/(2a) = 42/24 +- 30/24 = 7/4 +- 5/4#
#x = 12/4 = 3 and x = 2/4 = 1/2#
NOTE .
It is advised that you learn the improved quadratic formula.
a. It is easier to remember the formula by its graphic interpretation.
b. It is simpler for computing
c. It is easier to perform, when calculator are not allowed (exams/tests)