How do you find all values of k so that #2x^2+kx+12# can be factored?

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Answer 1 · 2016-12-05T23:32:56

#k in {+-10,+-11,+-12,+-24} #

The rule to factorise any quadratic is to find two numbers such that

#"product" = x^2 " coefficient "xx" constant coefficient"#
#"sum" \ \ \ \ \ \ = x " coefficient"#

So for #2x^2+kx+12# we seek two numbers such that

#"product" = 1*12 = 24#
#"sum" \ \ \ \ \ \ = k#

So if we looks at the factors of #24# and compute their sum we get

# {: ("factor1", "factor2", "sum"),(24,1,25),(12,2,12),(6,4,10),(3,8,11),(-24,-1,-25),(-12,-2,-12),(-6,-4,-10),(-3,-8,-11) :} #

Hence #k in {+-10,+-11,+-12,+-24} #