Question 177918
 D={{{b^2-4ac}}}  where D is the discriminant
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....zero, bē - 4ac = 0 ----->1 real (double)eg (x-3)(x-3) 
positive, bē - 4ac > 0 ----->2 real roots 
negative, bē - 4ac < 0 ----->2 complex roots 
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Equations taken in the form of ax+by+c=0
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I will do one and let you complete the rest
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37. x2 + 5x + 6 = 0 
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a=1,b=5,c=6
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{{{D=5^2-4((1)(6))=25-24=1}}}since D>0 we will have 2 real roots.

38. 3x2 - 4x + 3 = 0
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{{{(-4)^2-4(3)(3)=16-36=-20}}}D<0
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so 2 complex roots
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39. -2x2 - 5x + 4 = 0
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{{{(-5)^2-4(-2)(4)= 25+32=57}}}D>0 so 2 real roots
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40. 16x2 - 8x + 1 = 0
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{{{(-8)^2-4(16)(1)=64-64=0}}}so 1 real (double) root