Please help; i’m confused

The values of k that make the given equation having imaginary roots are:

k < -18, or (-∞,-18).

Step-by-step explanation:

Nature of the Roots of a Quadratic Equation

The standard representation of a quadratic equation is:

where a,b, and c are constants.

Solving with the quadratic formula:

The expression:

Is called the discriminant. The discriminant determines the nature of the roots of a quadratic equation as follows:

If d=0, there is only one real root.

if d>0, there are two different real roots

if d<0, there are two different imaginary (complex) roots

We are given the equation:

Comparing with the standard quadratic equation, we have:

a=-2, b=12, c=k

Calculating the discriminant:

If the equation has imaginary roots, then d<0, thus:

144 + 8k < 0

Subtracting 144:

8k < -144

Dividing by 8:

k < -18

The values of k that make the given equation having imaginary roots are: k < -18, or (-∞,-18).

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

your answer is  

d.

196.5 m2

step-by-step explanation: