For what value of k does the equation 4x^2−12x+k have only one solution?

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Answer 1 · 2018-05-18T04:12:36

#k=9#

.

#4x^2-12x+k=0#

If we have a quadratic function in the form of:

#ax^2+bx+c=0#

its solutions can be found by using the quadratic formula:

#x=(-b+-sqrt(b^2-4ac))/(2a)#

#b^2-4ac# is the determinant.

A quadratic function has one solution when its determinant is equal to #0#. In our problem:

#a=4, b=-12, c=k#

#b^2-4ac=(-12)^2-4(4)(k)=0#

#144-16k=0#

#144=16k#

#k=144/16=9#