Question

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

Answer 1

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)