ON PLATO Select the correct answer.
Which function has exactly one real solution?

Attached Below

Option A: f(x) = –3x² + 30x – 75

Step-by-step explanation:

To know which option is correct, we shall determine the discriminant of each equation since it gives the nature of the root of the equation.

Discriminant = b² – 4ac

NOTE:

1. If b² – 4ac < 0, it means the equation has no real roots.

2. If b² – 4ac = 0, it means the equation has only one real root.

3. If b² – 4ac > 0, it means the equation has two real roots

This can be obtained as follow:

For Option A:

f(x) = –3x² + 30x – 75

a = –3

b = 30

c = –75

Discriminant = b² – 4ac

Discriminant = 30² – (4 × –3 × –75)

Discriminant = 900 – 900

Discriminant = 0

Thus, the discriminant is equal to zero. This implies that the equation has only one real root.

For Option B:

f(x) = 2x² + 4x – 5

a = 2

b = 4

c = –5

Discriminant = b² – 4ac

Discriminant = 4² – (4 × 2 × –5)

Discriminant = 16 – (–40)

Discriminant = 16 + 40

Discriminant = 56

Thus, the discriminant is greater than zero. This implies that the equation has two real roots.

For Option C:

f(x) = 6x² + 11

a = 6

b = 0

c = 11

Discriminant = b² – 4ac

Discriminant = 0² – (4 × 6 × 11)

Discriminant = 0 – 264

Discriminant = – 264

Thus, the discriminant is lesser than zero. This implies that the equation has no real roots.

For Option D:

f(x) = –4x² + 9x

a = –4

b = 9

c = 0

Discriminant = b² – 4ac

Discriminant = 9² – (4 × –4 × 0)

Discriminant = 81 – 0

Discriminant = 81

Thus, the discriminant is greater than zero. This implies that the equation has two real roots.

Summary:

Option A : Only one real root.

Option B : Two real roots.

Option C : No real roots.

Option D : Two real roots.

The correct answer is option A.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

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step-by-step explanation: