For what value of k are there two distinct real solutions to the original quadratic equation (k+1)x²+4kx+2=0.

k ∈ (-∞,)∪(1,∞)

Step-by-step explanation:

For quadratic equations you can find the solutions with the Bhaskara's Formula:

A quadratic equation usually has two solutions.

If you only want real solutions the condition is that the discriminant () has to be greater than zero, this means:

Then we have the expression:

Now to find two distinct real solutions to the original quadratic equation we have to calculate the discriminant:

We got another quadratic function.

we can simplify the expression dividing both sides in 8.

We can apply Bhaskara's Formula except that the condition in this case is that the solutions have to be greater than zero.

Then,

The answer is:

For all the real values of k who belongs to the interval:

(-∞,)∪(1,∞)

there are two distinct real solutions to the original quadratic equation

-232

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.