SOLUTION: What is the largest value of k such that the equation x2 – 5x + k has at least one real root?
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Question 922555: What is the largest value of k such that the equation x2 – 5x + k has at least one real root?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
is in the form where , ,
Plug in , ,
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We will have at least one real solution when
Plug in . Solve for k.
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The answer as a fraction is
The answer as a decimal is
If you insist on having k be a whole number, then round to the nearest whole number to get
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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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The quadratic formula is:
The "discriminant" is:
For at least 1 real root,
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check:
suppose
which means 1 real root
and if , there are 2 real roots
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