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OpenStudy (ivonne123):
\[x^2-9x-136\]
jimthompson5910 (jim_thompson5910):
what are you trying to do exactly? Solve for x or factor? or something else?
OpenStudy (ivonne123):
Factor the trinomial.
jimthompson5910 (jim_thompson5910):
Let's compute the discriminant
D = b^2 - 4ac
D = (-9)^2 - 4(1)(-136)
D = 81 + 544
D = 625
Notice how the discriminant D = 625 is a perfect square
25^2 = 25*25 = 625 or put another way sqrt(625) = 25
So this implies that we can factor
jimthompson5910 (jim_thompson5910):
If the discriminant wasn't a perfect square, then you wouldn't be able to factor
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jimthompson5910 (jim_thompson5910):
you need to find two numbers that
A) multiply to -136
and
B) add to -9
OpenStudy (ivonne123):
all i think about it 9 x1 and 3 x 3
jimthompson5910 (jim_thompson5910):
what are some ways to multiply to -136?
OpenStudy (ivonne123):
8 and 17
jimthompson5910 (jim_thompson5910):
one of them has to be negative
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OpenStudy (ivonne123):
-17 & 8
jimthompson5910 (jim_thompson5910):
yes so that means x^2-9x-136 factors to (x-17)(x+8)