Answer:
a) k = 4
b) k < 4
Explanation:
For the quadratic equation
ax² + bx + c = 0,
the discriminant is
b² - 4ac.
The discriminant of a quadratic equation tells you the nature of the roots.
If the discriminant equals zero, there are 2 equal roots.
The the discriminant is greater than zero, there are 2 distinct, real roots.
For this quadratic equation,
x² + 4x + k = 0,
we have
a = 1; b = 4; c = k.
The discriminant is
b² - 4ac = 4² - 4(1)k) = 16 - 4k
a)
For 2 equal roots, we need the discriminant to equal zero.
16 - 4k = 0
16 = 4k
k = 4
b)
For 2 distinct, real roots, we need the discriminant to be greater than zero.
16 - 4k > 0
-4k > -16
k < 4