Question 922555
{{{x^2-5x+k}}} is in the form {{{ax^2+bx+c}}} where {{{a = 1}}}, {{{b=-5}}},{{{c = k}}}



{{{D = b^2 - 4ac}}}



{{{D = (-5)^2 - 4*1*k}}} Plug in {{{a = 1}}}, {{{b=-5}}},{{{c = k}}}



{{{D = 25 - 4k}}} 



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We will have at least one real solution when {{{D >= 0}}}



{{{D >= 0}}}



{{{25 - 4k >= 0}}} Plug in {{{D = 25 - 4k}}}. Solve for k.



{{{25 >= 4k}}}



{{{4k <= 25}}}



{{{k <= 25/4}}}



{{{k <= 6.25}}}



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The answer as a fraction is {{{k <= 25/4}}}



The answer as a decimal is {{{k <= 6.25}}}



If you insist on having k be a whole number, then round to the nearest whole number to get {{{k = 6}}}



In terms of a decimal, the largest k can be is 6.25 or 6 (depending on if you want a whole number or not).




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Let me know if that helps or not. Thanks.


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