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CONSIDER THESECCOND DEGREE EQUATION (4-K)X*X+(2K+4)X+(8K+1)=0 A)FIND DISCRIMINANT B)IS THE DISCRIMINANT SECOND DEGREE EQUATION.WHY? C)FOR WHAT VALUE OF K WILL THIS EQUATION BE A PERFECT SQARE?

Here, a = 4 - k ; b = 2k + 4  ; c = 8k + 1
discriminant = b2 - 4ac
                   =(2k + 4)2 - 4(4 - k)(8k + 1)
                   = 4k2 + 16k + 16 - 4(32k + 4 - 8k2 - k)
                   = 4k2 + 16k +16 - 128k - 16 + 32k2 + 4k
                   = 36k2 - 108 k ,which is a perfect square.
If the equation is a perfect square , b2 - 4ac = 0 ,
36k2 - 108 k = 0
ie , 4k(9k - 27) = 0
k = 0 or 9k - 27 = 0
               k = 27 / 9 = 3

      


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