Question 196155: What are the values of m such that 4x2 - 4mx + 4m - 3 is perfect square trinomial?
a.) -1, -3
b.) 1,-3
c.) 1,3
d. -1, 3
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 4x^2 - 4mx + (4m -3)
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4 ( x^2 -mx +(m-3/4) )
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Remember perfect square is (1/2 * 2nd coefficient)^2 = (3rd coefficient)
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or,,,,(-m/2)^2 = m-.75
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m^2 /4 =m-.75
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mult by 4
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m^2 = 4m -3
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m^2 -4m +3 =0
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( m-3)(m-1) =0
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m-3 =0,,,,m=3
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m-1 =0,,, m=1
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Therefore answer (C)
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Checking
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m=1, 4x^2 -4(1)x +(4(1)-3)
4x^2 -4x +1
4(x^2 -x +1/4)
4( x-1/2) (x-1/2)
4(x-1/2)^2,,,,,,ok
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m=3,,, 4x^2 -4(3)x +(4 (3) -3)
4x^2 -12x +9
4 ( x^2 -3x +9/4)
4( x-3/2)(x-3/2)
4 (x-3/2)^2,,,,,ok
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