The equation x^2-2kx+7k-12=0 has real and equal roots. Calculate k !

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x^2 - 2kx + 7k - 12 = 0

if both roots are real and equals, then the equation has one solution. Then the discrminant must be zero.

==> delta = b^2 - 4ac = 0

==> 4k^2 - 4(1)(7k-12) = 0

==> 4k^2 - 28k + 48 = 0

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x^2 - 2kx + 7k - 12 = 0

if both roots are real and equals, then the equation has one solution. Then the discrminant must be zero.

==> delta = b^2 - 4ac = 0

==> 4k^2 - 4(1)(7k-12) = 0

==> 4k^2 - 28k + 48 = 0

Divide by 4:

==> k^2 - 7k + 12 = 0

==> (k -4)(k-3) = 0

Then there are two solutions:

k1 = 4

k2= 3

Approved by eNotes Editorial Team