Posted by Math Lab on 11/10/2008, 2:19 pm, in reply to "mth 158"
164.106.208.1
Your 1st step was in the right direction.
For real and equal you do b2 - 4ac = 0 and then solve. Doing that we get
(-2k)2 - 4(1)(7k+8) = 0
4k2 + 28k - 32 = 0 then factor out a 4
4(k2 + 7k - 8) = 0 then factor again
4(k + 8)(k - 1) = 0 then set each part equal to zero and solve for k
k + 8 = 0 and k - 1 = 0 giving you
k = -8 and k = 1
Then for real and unequal you want b2 - 4ac > 0 so we take what we have from part a and make our intervals based on the values of k that made b2 - 4ac = 0. so our intervals are (negative infinity, -8), (-8,1), and (1, infinity) pick a number in each interval to see if that interval is positive or negative. The positive ones are the intervals we want. so for the interval (negative infinity, -8) we can pick -10 for k and plug it in to 4k2 + 28k - 32 and we get 88 and for a number in (-8,1) we pick 0 and get -32 and for a number in (1,infinity) we pick 2 and get 40 so any number in the interval (negative infinity, -8) or (1,infinity) will give use 2 real unequal roots.
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