Q. 383.7( 3 Votes )

Find m if (

Answer :

For roots to be equal, determinant must be equal to 0.


in case of quadratic eq., ax2 + bx + c = 0


determinant(D) = b2 – 4ac


According to the question,


a = m – 12


b = 2(m – 12)


c = 2


So, 4(m – 12)2 – 4(m – 12)x2 = D


4(m2 + 144 – 24m) – 8(m – 12) = 0


4m2 + 576 – 96m – 8m + 96 = 0


4m2 – 104m + 672 = 0


m2 – 26m + 168 = 0


m2 – 12m – 14m + 168 = 0


m(m – 12) – 14(m – 12) = 0


(m – 12)(m – 14) = 0


m = 12 or m = 14


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