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stich3 [128]
3 years ago
6

Create a number line

Mathematics
1 answer:
wel3 years ago
4 0

Step-by-step explanation:

is it correct ?? think that d answer is helpful to u

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?
lys-0071 [83]

Answer:

2

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

3x^2-(3k-2)x-(k-6) \text{ with }k=2:

3x^2-(3\cdot 2-2)x-(2-6)

3x^2-4x+4

I'm going to solve 3x^2-4x+4=0 for x using the quadratic formula:

\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}

\frac{4\pm \sqrt{16-16(3)}}{6}

\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}

\frac{4\pm 4\sqrt{-2}}{6}

\frac{2\pm 2\sqrt{-2}}{3}

\frac{2\pm 2i\sqrt{2}}{3}

Let's see if uv=u+v holds.

uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}

Keep in mind you are multiplying conjugates:

uv=\frac{1}{9}(4-4i^2(2))

uv=\frac{1}{9}(4+4(2))

uv=\frac{12}{9}=\frac{4}{3}

Let's see what u+v is now:

u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}

u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}

We have confirmed uv=u+v for k=2.

4 0
2 years ago
There are 72 students in the marching band. The ratio of girls to boys is 19 to 17.
8090 [49]

Answer:

34 boys

Step-by-step explanation:

72 students

G-19:B-17 Ratio

19 + 17 = 36

72/36 = 2

19 x 2 = 38

38 girls

17 x 2 = 34

34 boys

4 0
2 years ago
4 to 7 equals 21 to what ​
Margaret [11]
Can you show the whole question
8 0
2 years ago
Read 2 more answers
Please help with math ​
irakobra [83]

Answer:

5 and 6

Step-by-step explanation:

You have to find two numbers (in the chart) that have a difference of 3/8.

This is just one possiblity, there are other correct answers.

There is size 5 and 6. 9 and 4/8-9 and 1/8=3/8.

8 0
3 years ago
Write the equations for the graphs below (worth 5 points) ​
serg [7]
Answers:

10) y= 1/2x - 2
11) y= 2x + 3
12) y= 2/3x - 4

I found this by using y=mx+ b
3 0
2 years ago
Read 2 more answers
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