SOLUTION: For what values of k does 2x^2 - 5x - k = 0 have no real roots? Can you please help me out? Thanks so much in advance:)

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Question 825876: For what values of k does 2x^2 - 5x - k = 0 have no real roots?
Can you please help me out? Thanks so much in advance:)

Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Use the quadratic formula




the roots are imaginary when
is negative. Since is always positive.



answer
( note that I had to reverse the inequality sign
when I divided by a negative number )
---------------
Suppose




That means there is 1 real root
---------------------------
Suppose or





That means there are 2 imaginary roots

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

For what values of k does 2x^2 - 5x - k = 0 have no real roots?
Can you please help me out? Thanks so much in advance:)

For values of k to have no real roots, the DISCRIMINANT MUST BE < 0 (negative). Therefore, we set the
DISCRIMINANT as negative, and solve.
DISCIMINANT: , with: a = 2 ; b = - 5 ; c = - k
Then, becomes:




You can do the check!!
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