Find the constant k so that the quadratic equation 2x2 + 5x - k = 0 has two real solutions.

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 2x2 + 5x - k = 0

If the function has two real solutions , then delta must be a positive number greater than 0:

We know that:

delta = b^2 - 4*a*c > 0

Such that:

a = 2   b = 5     c = -k

Let us calculate:

delta...

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 2x2 + 5x - k = 0

If the function has two real solutions , then delta must be a positive number greater than 0:

We know that:

delta = b^2 - 4*a*c > 0

Such that:

a = 2   b = 5     c = -k

Let us calculate:

delta = 5^2 - 4*2*-k  > 0

==> 25 + 8k > 0

Now subtract 25 from both sides:

==> 8k > -25

Now we will divide by 8:

==> k > -25/ 8

Then k values shoul bs greater that - 25/8 in order for the function to have two real roots.

 

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