How do you solve using the quadratic formula for y = 12x^2 - 35x + 8?

1 Answer
Nghi N.
May 16, 2015

y = 12x^2 - 35x + 8 = 0

D = d^2 = b^2 - 4ac = 1225 - 384 = 841 -> d = +- 29

x = 35/24 + 29/24 = 64/24 = 8/3

x = 35/24 - 29/24 = 6/24 = 1/4

There is another way: solving by the new Transforming Method (Google , Yahoo Search) that may be faster and not boring, especially when you can't use calculator.
y = 12x^2 - 35x + 8
Transformed equation : y' = x^2 - 35x + 96 (a.c = 12(8) = 96)
Solve y' by composing factor pairs of (96). Proceed: (2, 48)(3, 32).
This last sum is 35 = -b. Then its 2 real roots are: p' = 3 and q' = 32. Back to original equation, the 2 real roots are: p = (p')/a = 3/12 = 1/4, and q = (q')/a = 32/12 = 8/3.

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