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Ray Of Light [21]
3 years ago
11

How many real-number solutions does 4x² + 2x +5=0 have?

Mathematics
1 answer:
Allisa [31]3 years ago
8 0

Answer:

c. zero

Step-by-step explanation:

The expression on the left of the equal sign is a polynomial of degree 2. (The highest power of x is 2.) A polynomial of degree 2 is called a "quadratic." Values of the variable (x, in this case) that make the value of the quadratic be zero are called "zeros" or "roots" of the quadratic.

Every polynomial has as many roots as its degree. So, a second degree polynomial (quadratic) will have two roots. The roots may be real numbers, or they may be complex numbers. For polynomials of degree higher than 2, there may be some roots of each kind.

This question is asking, "How many roots of this quadratic are real numbers?"

___

There are several different ways you can figure out the answer to this question. One of the simplest is to graph the quadratic. (See attached.) You can see that the graph of the quadratic never has a y-value of zero, so there are no (real) values of x that will be solutions to this equation.

The two solutions are -0.25±i√1.1875. The "i" indicates that portion of the number is imaginary, and the entire number (real part plus imaginary part) is called a "complex" number. Both solutions for this quadratic are complex, not real.

__

Another way you can answer this question is to compute what is called the "discriminant." The roots of every quadratic of the form ax^2+bx+c can be found using the formula ...

x = (-b±√(b^2-4ac))/(2a)

For this quadratic, the values of a, b, and c are 4, 2, and 5, respectively. Then the formula becomes ...

x = (-2±√(2^2 -4·4·5))/(2·4) = (-2±√-76)/8

The value under the radical sign is the "discriminant." When it is negative, as here, the value of the square root is an imaginary number (not a real number), so the roots are complex. When the discriminant is zero, the two roots have the same value; when it is positive, there are two distinct roots.

There are zero real number solutions to this equation.

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Answer:

$45.8

Step-by-step explanation:

32.06 / 14= 2.29

2.29x20=45.8

8 0
2 years ago
The population of fish in a lake doubles every decade.
Kaylis [27]

Answer:

48,000

Step-by-step explanation:

3,000 x 2 = 6000 (decade one)

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6 0
3 years ago
Read 2 more answers
Which of the following describes the correct process for solving the equation 3x+6=21 and arrives at the correct solution?
My name is Ann [436]
The correct solution is C

Subtract 6 from both sides of the equation
        3x + 6 - 6 = 21 - 6
        3x = 15

Then divide both sides by 3

       \frac{3x}{3}   =    \frac{15}{3}
       
       x = 5

4 0
3 years ago
A box of multi-color paper clips contains 25 red clips, 15 blue clips, 15 green clips and 20 pink clips. If Roy
kolbaska11 [484]

Answer:

8/15

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen added to the probability that the event will not happen gives 1. In other words, the outcome of a probability cannot exceed 1.

The probability that an event a will happen or that another independent event  b will happen is the sum of the probability that a will happen to the probability that b will happen.

Given that there are 25 red clips, 15 blue clips, 15 green clips and 20 pink clips,

total number of clips available

= 25 + 15 + 15 + 20

= 75

probability of picking a

red paper clip = 25/75

blue paper clip = 15/75

Probability of selecting red or  blue paper clip

= 25/75 + 15/75

= 40/75

= 8/15

3 0
4 years ago
Simplify the following expression completely, where x 20.
Katena32 [7]

Answer:

Thats gibrish what the heckity heck

Step-by-step explanation:

learn from duolingo

5 0
3 years ago
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