1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergejj [24]
3 years ago
15

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?

Mathematics
1 answer:
lys-0071 [83]3 years ago
4 0

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.

You might be interested in
An item costs $300 before tax, and the sales tax is $9.90 . Find the sales tax rate. Write your answer as a percentage.
Step2247 [10]

Answer:

3.33%

Step-by-step explanation:

9.90/300=0.033

8 0
2 years ago
joe weighs 20lbs.less yhantwice jeffs weight.if jeff would gain 10lbs.,then together they wouldweigh 250lbs. how much does each
masya89 [10]
So,

Let x represent Joe's weight and y represent Jeff's weight.

"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250

We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250

Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250

We will use Elimination by Substitution.
2y - 20 + y + 10 = 250

Collect Like Terms.
3y - 10 = 250

Add 10 to both sides.
3y = 260

Divide both sides by 3.
Jeff's\ weight = 86 \frac{2}{3} \ lbs.

Substitute again.
x = 2(86 \frac{2}{3} )-20

Multiply.
x = 173 \frac{1}{3} -20

Subtract.
Joe's\ weight = 153 \frac{1}{3}\ lbs.

Check.

"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.

Joe's\ weight\ is\ 153 \frac{1}{3} \ lbs.
Jeff's\ weight\ is\ 86 \frac{2}{3} \ lbs.
3 0
3 years ago
What is y=3x^2-2 in vertex form
Nata [24]
\bf \qquad \qquad \textit{parabola vertex form}
\\\\\\
y=a(x-{{ h}})^2+{{ k}}\\
x=a(y-{{ k}})^2+{{ h}}\qquad\qquad  vertex\ ({{ h}},{{ k}})\\\\
-----------------------------\\\\
y=3x^2-2\iff y = 3(x-0)^2-2
3 0
3 years ago
Find the product.<br><br> (-3ab2)3<br><br> -27 a3b6<br> -9 a3b5<br> -23 a2b2<br> 27 ab
7nadin3 [17]

Answer:

a) -27 a³ b⁶

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given ( -3 ab² )³

By using  (ab )ⁿ = aⁿ bⁿ      

   ( -3 ab² )³ = (-3)³ a³ (b²)³

Again , using formula   (a^{m} )^{n} = a^{mn}

                    =   -27 a³ b⁶

6 0
3 years ago
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup o
Alik [6]

Answer:

To maximize profit, the amount of each type of coffees made are;

The number of regular latte made = 52 cups

The number of low-fat latte made = 48 cups

Step-by-step explanation:

The given parameters are;

The number of espresso in a regular latte = 1 shot

The number of cups of 2% milk in regular latte = 1 cup

The amount of whipped cream in a regular latte = 0.5 cup

The number of cups of skim milk in the low-fat latte = 1.25 cup

The number of espresso in a low-fat latte = 1 shot

The amount of whipped cream in a low-fat latte = 0 cup

The number of cups of espresso in the journey = 100 shots

The number of cups of skim milk in the journey = 60 cups

The number of cups of 2% milk in the journey = 60 cups

The amount of profit the airline makes on each regular latte = $1.58

The amount of profit the airline makes on each low-fat latte = $1.65

Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;

x ≤ 30/0.5 = 60

x ≤ 60

y ≤ 60

y ≤ 60/1.25 = 48

∴ y ≤ 48

x + y ≤ 100

Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made

Therefore, the number of low-fat latte made, y = 48

Therefore, the number of regular latte made, x ≤ 100 - 48 = 52

For maximum profit, the maximum number of low-fat latte, 'x', should be made

Therefore, x = 52

The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte

5 0
3 years ago
Other questions:
  • Is 4:6 equivalent to 2:3
    5·1 answer
  • How are the ratios 100/2, 150/3, 175/3.5, 200/4 related to 50/1?
    10·1 answer
  • Which on of these numbers is not like the others? 25, 16, 49, 63, 81
    14·1 answer
  • lin read 3/8 of a magazine article on monday and 1/8 of article tuesday. what fraction of the article did she read on monday and
    8·2 answers
  • Use the product to simplify the expression. write your answer in exponential notation.
    7·2 answers
  • Suppose that x and y vary inversely. write a function that models each inverse variation.
    11·1 answer
  • What is the circumference of the circle r=4ft
    10·2 answers
  • I have more im about to post it after this :D plz help and explain
    9·2 answers
  • Find the slope for line with the points (3,9) and (7,9)
    8·1 answer
  • Evaluate - 1 - ( - z ) where z = -2
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!