Answer:
3.2 is the highest value for k that will yield a non-negative discriminant
Step-by-step explanation:
For an equation to have real numbers as solutions, its discriminant (delta value) must be bigger than zero since there are no real square root solutions for negative numbers.
[tex]x_{1} =\frac{-b +\sqrt{\Delta} }{2a}\\x_{2} =\frac{-b -\sqrt{\Delta} }{2a}[/tex]
In this case, the discriminant is given by:
[tex]\Delta = (-8)^{2} - 4*5*k \\\Delta = 64 - 20*k \\[/tex]
For k =3.2
[tex]\Delta = 64 - 64 = 0 \\[/tex]
As shown above, 3.2 is the highest value for k that will yield a non-negative discriminant and, therefore, if k > 3.2 the solutions of the expression are not real numbers.
