How do you factor and solve #x^2−(7/2)x+3/2=0#?

1 Answer
Nghi N.
May 20, 2016

(1/2)(x - 3)(2x - 1)

Explanation:

#y = x^2 - (7/2)x + 3/2 = 0#
Find 2 fractions knowing sum #(b = -7/2)# and product #(c = 3/2)#.
By guessing, they are the 2 fractions: #-3/1 and -1/2#.
Sum:# -3/1 - 1/2 = -6/2 - 1/2 = -7/2#
Product:# (-3/1)(-1/2) = 3/2#
Factored form of y.
#y = (x - 3)(x - 1/2) = (1/2)(x - 3)(2x - 1)#
There are 2 real roots: x = 3 and x = 1/2

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