Which number is the largest? 7.2 ⋅ 10−6, 3.09 ⋅ 103, 2.04 ⋅ 104, 5 ⋅ 103

Suppose the roots of the polynomial $x^2 - mx + n$ are positive prime integers (not necessarily distinct). Given that $m < 20

Vsevolod [243]

Answer:

18 values for n are possible.

Step-by-step explanation:

Given the quadratic polynomial:

$x^2 - mx + n$

such that:

Roots are positive prime integers and

$m < 20$

To find:

How many possible values of $n$ are there ?

Solution:

First of all, let us have a look at the sum and product of a quadratic equation.

If the quadratic equation is:

$Ax^{2} +Bx+C$

and the roots are: $\alpha$ and $\beta$

Then sum of roots, $\alpha+\beta = -\frac{B}{A}$

Product of roots, $\alpha \beta = \frac{C}{A}$

Comparing the given equation with standard equation, we get:

A = 1, B = -m and C = n

Sum of roots, $\alpha+\beta = -\frac{-m}{1} = m$

Product of roots, $\alpha \beta = \frac{n}{1} = n$

We are given that $m$

$\alpha$ and $\beta$ are positive prime integers such that their sum is less than 20.

Let us have a look at some of the positive prime integers:

2, 3, 5, 7, 11, 13, 17, 23, 29, .....

Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.

So, possible combinations and possible value of $n (= \alpha \times \beta)$ are:

$1.\ 2, 2\Rightarrow n = 2\times 2 = 4\\2.\ 2, 3 \Rightarrow n = 6\\3.\ 2, 5 \Rightarrow n = 10\\4.\ 2, 7\Rightarrow n = 14\\5.\ 2, 11 \Rightarrow n = 22\\6.\ 2, 13 \Rightarrow n = 26\\7.\ 2, 17 \Rightarrow n = 34\\8.\ 3, 3\Rightarrow n = 3\times 3 = 9\\9.\ 3, 5 \Rightarrow n = 15\\10.\ 3, 7 \Rightarrow n = 21\\$

$11.\ 3, 11\Rightarrow n = 33\\12.\ 3, 13 \Rightarrow n = 39\\13.\ 5, 5 \Rightarrow n = 25\\14.\ 5, 7 \Rightarrow n = 35\\15.\ 5, 11 \Rightarrow n = 55\\16.\ 5, 13 \Rightarrow n = 65\\17.\ 7, 7 \Rightarrow n = 49\\18.\ 7, 11 \Rightarrow n = 77$

So,as shown above 18 values for n are possible.

3 0

3 years ago

Luis earns a base salary of $150.00 every week with an additional 14% percent commission on everything he sells. Luis sold $6050

timama [110]

$150(1 + 0.14) = x \\ 6050 \div x = y$
hope that helps

4 0

2 years ago

How do I solve 3/10+2.125 Converted into fractions

ahrayia [7]

Answer:

97/40

Step-by-step explanation:

so 2.125= 17/8

3/10+17/8 need to find common denominator so

times 8/8 to 3/10

times 10/10 to 17/8

24/80+170/80= 194/80 (common denominator so can add)

divide 194/80 because want reduce form

97/40 is the answer

(When i look at it now i can just time 4/4 and 5/5 but its ok this still gets the answer)

3 0

3 years ago

What is the sum of 2x^2-5x-2and 4x^2-6x+8

rjkz [21]

Step-by-step explanation:

this should be correct but im not 100%sure

6 0

2 years ago

The stock of Company A lost $4.17 throughout the day and ended at a value of

Anit [1.1K]

Answer:

4%

Step-by-step explanation:

After losing 4.17, it came down to 100.08, so the opening price was:

100.08 + 4.17 = 104.25

To find percentage decline, we find the ratio of the "change" (which is 4.17) divided by the opening (original) price, which is 104.25. Then we multiply that fraction by 100 to get our percentage decline.

So,

$\frac{4.17}{104.25}*100=4$

Thus, the

percentage decline = 4%

4 0

2 years ago