Question 204946: Find b^2-4ac adn the number of real solutions to this equation:
9m^2 + 16 = 24m
I am confused !!! Can you help me? :-)
Thanks,
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Let D = Discriminant = (b^2 -4 ac)
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basic form is ax^2 +bx+c =0
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when D=0,,,one solution, line touches x axis one time
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when D>0,,,two solutions, line intercepts x axis 2 times
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when D<0,,,no (REAL) solutions, line does not touch x axis
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in this case,, 9m^2 +16 = 24m
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9m^2 -24m +16 =0
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D= { (-24)^2 -4(9)(16)} = {576 - 576} =0,,,,,and one solution
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solving for m using the quadratic equation demonstrates the use of D
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m=[-b +/- sqrt D] /2(a) = {-(-24) +/- sqrt(0) }/2(9)= 24/18 = 4/3=1 1/3
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NOTE: @ D=0, m= {(-b) +/- 0 }/2a = -b/2a,,,,or one number
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@ D >0,,m= { (-b) +/- sqrt(+#) } /2a,,,or two #'s
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@ D <0,,,m= { (-b) +/- sqrt(-#) }/2a = complex number
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to check : factor,,, 9m^2 -24m +16,,(3m-4)(3m-4),,
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set equal to zero,,,,3m-4=0,,,m=4/3 (twice),,,,but only one solution
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