Answer: Choice C) k < 4
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Step-by-step explanation:
Recall the discriminant formula is
d = b^2 - 4ac
which is the stuff found under the square root in the quadratic formula.
If d > 0, then the equation ax^2+bx+c = 0 will have two different real number roots.
So,
d > 0
b^2 - 4ac > 0
4^2 - 4(1)(k) > 0
16 - 4k > 0
16 > 4k
4k < 16
k < 16/4
k < 4 which points us to choice C
For example, if k = 0, then the equation x^2+4x+k = 0 becomes x^2+4x = 0. This has the two different roots of x = 0 and x = -4.