Question #2d2ff

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Answer 1 · 2017-03-19T18:39:36

#q = 6 and q = -6#

Let #r_1 =# the first root
Let #r_2 = # the second root
Given: #r_1-r_2=2#

#(x - r_1)(x - r_2) = x^2 - qx + 8#

#x^2 -r_2x -r_1x + r_1r_2 = x^2-qx+8#

#-r_1-r_2 = -q#
#r_1-r_2=2#
#r_1r_2=8#

Substitute for #r_2 = 8/r_1#:

#-r_1-8/r_1 = -q#

#r_1-8/r_1=2#

#q = r_1+8/r_1" [1]"#

#r_1^2-2r_1-8=0" [2]"#

Factor equation [2]:

#(r_1-4)(r_1+2)#

#r_1 = 4 and r_1 = -2#

#q = 4 + 8/4 and q = -2+8/-2#

#q = 6 and q = -6#