determine the value of k for which the quadratic equation 4x sq.-3kx+1=0 has equal roots

The given quadratic equation is,4x2 - 3kx + 1 = 0comparing it with standard equation that is ax2 + bx + c = 0 , we geta = 4  ;  b = -3k   ;  c = 1Now, D = b2 - 4ac = (-3k)2 - 4(4)(1) = 9k2  - 16for equal roots, D = 0so,  9k2  - 16 = 0   k2 = 169  k = ±43

  • 4

4x2 - 3kx + 1 = 0

a = 4 , b = -3kx , c = 1

since the eq. has equal roots,

b2 - 4ac = 0

(-3k)2 - 4(4)(1) = 0

9k2 - 16 = 0

9k2 = 16

k2 = 16/9

k = 4/3 or k = - 4/3

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