If x=k is one of the solution of 2x2+5x-k=0 find the two possible values of k

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Solution

2x²+ 5x + k = 0

The quadratic equation is
x= (-b ±√(b²-4ac))/2a

If b²-4ac is less than zero the roots are not real.

a=2, b=5, c = k

b²-4ac<0
5²-4(2)k <0
25-8k <0
-8k < -25
k>25/8
k>3.125

In interval notation: (3.125, ∞)

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