find the value of k if the roots
of 3x²-5x+k=0, differ by 2​

Answers

Answer 1

By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as

3x ² - 5x + k = 3 (x - a) (x - b)

and upon expanding, we have

3x ² - 5x + k = 3x ² - (a + b) x + ab

Two polynomials are equivalent if their coefficients are equal, so

a + b = 5

ab = k

We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :

a + (a - 2) = 5

2a - 2 = 5

2a = 7

a = 7/2

Solve for b :

b = 7/2 - 2

b = 3/2

Solve for k :

k = 7/2 × 3/2 = 21/4


Related Questions

Which of the following ordered pairs is a solution of the system of inequalities?
y > 2x2 – 8
y ≤ –x2 – 3x + 4
Question 5 options:

A)

(4, –3)

B)

(–3, –2)

C)

(5, 0)

D)

(0, –5)

Answers

9514 1404 393

Answer:

  D)  (0, -5)

Step-by-step explanation:

A graphing calculator is helpful. It shows that the point (0, -5) is in the solution spaces of both inequalities.

__

If we consider only the case of x=0, then the solution space reduces to ...

  -8 < y ≤ 4 . . . . . the constants of the two inequalities

Here, it is easy to see that y=-5 is in the solution space.

  (0, -5) is a solution

Es fills his sport bottle wit 1.2 liter of water how much milliliters of water is in ed sport bottle

Answers

There is 1200 mL in his bottle

6. The base of a pyramid is a triangle whose base is 11 yards and height is 19
yards. Determine the volume of the pyramid, if its height is 7 yards. Round
your answer to two decimal places.

Answers

Pretty sure volume would be 487.67

Because volume= lwh/3

PLSSS ANSWER JUST PUT THE NUMBER OF THE QUESTION THEN THE ANSWER PLS HELP ITS OVERDUE AND IM GONNA FAIL 7TH GRADE :(
I WILL GIVE BRAINLIEST EVERYONE KEEPS GIVING ME RANDOM LINKS IM CRYIING :( I WOULD BE SO GRATEFUL IF U HELPED UR A LIFE SAVER

Answers

Answer:

Alright but first

How is this 7th grade stuff?

I thoguh yall were doing algebra. But it kinda looks like it but here’s a brief explanation anyway.

If you dont know a vualure, use other surrounding it to help you sovle this final thingy. Like if its division, multiply. addditon, subtract. multiply, Davison. Just tdo inver properties on both sides and isolate the number that x in it Either be dividing or multiplying. When your left with a final value just solve, whatever thing that lies next to that equal sign is your answer.

2) 6

3) -36

4) 40

5) 9

6) -4

7) 63

8) -48

9) -5

10) -7

Please help me with this question if you can

Answers

Answer:

exterior angle = the sum of two remote interior angles

14x + 1 = 89 + 5x - 7

=> 9x = 81

=> x = 9

substitute x = 9 into angle H (5x - 7)

=> 5(9) - 7 = 45 - 7 = 38

Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathroom scales. The readings on 28 of the scales were too light, and the readings on the other 22 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight? Find the P-value and state a conclusion. The P-value is . Round the answer to four decimal places. We cannot conclude that more than half of bathroom scales underestimate weight.

Answers

Answer:

the P-value = 0.1977

conclusion: Since the p-value is not small;

we reject null hypothesis

hence, the data does not support claim that more than half of the bathroom scales underestimate weight.

Step-by-step explanation:

 Given the data in the question;

let X represent the number of successes ( the weight is underestimated ) in n independent Bernoulli trials, each with the success probability p

X - Bin( n,p).

so

Null hypothesis             H₀ : p ≤ 0.5

Alternative hypothesis Hₐ : p > 0.5

now, compute np₀ and n( 1 - p₀ )

np₀ = (50)(0.5)

np₀ = 25

n( 1-p₀ ) = (50)(1 - 0.5)

n( 1-p₀ ) = 25

we can see that both values are greater than 10.

∴ the sample proportion is approximately normally distributed;

P" - N ( p₀, [tex]\frac{p_{0}(1-p_0)}{n}[/tex] )

sample proportion p" = 28/50 = 0.56

standard deviation will be;

σ[tex]_{p"[/tex] = √( p₀(1-p₀) / n )

σ[tex]_{p"[/tex] = √( 0.5(1-0.5) / 50 )

σ[tex]_{p"[/tex] = √( 0.25 / 50 )

σ[tex]_{p"[/tex] = 0.07071

Next is the Z-score

z = p" - p₀ / σ[tex]_{p"[/tex]

z =  0.56-0.5 / 0.07071

z = 0.06 / 0.07071

z = 0.85

from table,

the probability that a standard normal random variable takes on a value greater than 0.85 is approximately 0.1977

Therefore, the P-value = 0.1977

conclusion: Since the p-value is not small;

we reject null hypothesis

hence, the data does not support claim that more than half of the bathroom scales underestimate weight.

p = 0.197663

State the discriminant of 6x2-2x+K, and state for which values of K would result in two different solutions.

Answers

A..........

Step-by-step explanation:

What is the equation of the following line? Be sure to scroll down first to see all answer options. (2,10) (0,0)​

Answers

Answer: y=5x

Step-by-step explanation: Slope= 10/2=5 Plugged it in equation y=mx+b and solved for b to get b=0

Please help extremely important!!

Answers

Sorry I’m not sure...

Flask Company reports net sales of $2,620 million; cost of goods sold of $2,230 million; net income of $450 million; and average total assets of $2,090 million. Compute its total asset turnover.

Answers

Answer:

to me it is at least $3000

Which of the following equations will produce the graph shown below?

A. x^2 = 8y
B. x^2= -8y
C. x-1/8y^2= 0
D. y= 1/2x^2

Answers

C. I think cause I have a Duda in that iam not smart but i think it’s c

Answer: The correct answer is C

x-1/8y^2=0

Step-by-step explanation: i took the test and got it right

Each figure below represents a fraction. Which figure is NOT equivalent to the others

Answers

The full question with the answer options is as follows:

Each figure below represents a fraction. Which figure is NOT equivalent to the others?

the answer options are as follows:

a.  [tex]\frac{2}{3}[/tex]

b.  [tex]\frac{4}{6}[/tex]

c.  [tex]\frac{3}{4}[/tex]

d. [tex]\frac{8}{12}[/tex]

Answer:

The correct answer is c:

Step-by-step explanation:

To know when two or more fractions are equivalent, we must multiply the numerator of one fraction by the denominator of the other fraction, the result must be the same value.

[tex]\frac{2}{3} x \frac{4}{6}[/tex] =   (2x6) =12   ;  (3x4)=12

[tex]\frac{2}{3} x \frac{8}{12}[/tex] = (2x12)=24 ;    (3x8) =24

[tex]\frac{4}{6} x \frac{8}{12}[/tex] = (4x12)=48;     (6x8)=48

helpppppppppppppppppp

Answers

Answer:

38º

Step-by-step explanation:

the angles that are across from each other like

the 38º and <6<2 and <4<3 and <5<1 and <7

are equal.

So, <6 = 38º (This is also because of the Vertical Angle Theorem / VAT)

HELP [14] pOINTS LOOK AT THE PHOTO

Answers

Answer:

I THINK the answer is , I'm really not confident on this one.

Answer:

They are perpendicular ⊥

Step-by-step explanation:

Please help me.......... ​

Answers

Answer:

I think it's 4.5

Step-by-step explanation:

I divided the servings by the packages and I got 4.5 for each of them.

Hi anyone here for talking​

Answers

Answer:

yessssssssss.........

Find the value of y.
3 cm
5 cm
X
6 cm
у
2 cm
3 cm
y = [?] cm
Enter a decimal rounded to the nearest tenth.

Answers

Answer: 4.3

Step-by-step explanation:

11x2=22

22/3= 7.3

7.3-3= 4.3

URGENT WILL GIVE BRAINLIEST

Answers

Answer:

40

Step-by-step explanation:

Simplify Help me please with this question!!!!!

Answers

F/3= -115 hope this helps bro

Which set of shapes could you use to form a net for a
triangular prism?

O 5 triangles
О 4 triangles, 1 rectangle
O 3 triangles, 2 rectangles
O 2 triangles, 3 rectangles

Answers

Draw a triangular prism and you see 2 triangles on the end with 3 rectangle connecting them
So the answer is: 2 triangles, 3 rectangles

Write down an irrational number with a value between 6 and 7.​

Answers

Answer:

Three irrational numbers between 6 and 7 are

i )6.2020020002...

ii) 6.5010010001....

iii)6.9010010001.... etc.

•••♪

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

3 irrational numbers with a value between 6 & 7 can be :-

6.101001000....6.533533353333....6.122122212222...

Someone please answer this without trying to send me a link

Answers

Answer:

y=-2x+5

Step-by-step explanation:

y=-2x+5

5/9 divided by 8/= ?

Answers

the answer is 0.06944 or as a fraction 5/72

Your credit card has an annual percentage rate of 16.99%. The current balance on your credit card is $2,140.40. What is your new account balance after finance charges are applied?

Answers

The answer is 1776.74604

Will give BRAINLIEST if you help me out

Answers

The x coordinate P is on is -1.5

A spinner has 3 equal sections labeled X, Y, and Z. Jinghua spins this spinner twice. Which represents all the possible outcomes for Jinghua?

Select one:


XY, XZ, YX, YZ, ZX, ZY


XX, XY, XZ, YX, YY, YZ, ZX, ZY, ZZ


X, Y, Z


XX, YY, ZZ
acually anwser or i'll report u

Answers

Answer:

XX, YY, ZZ

Step-by-step explanation:

Please calculate the probability using the following equations (in document)

Answers

Substitute u = t ³/2592 and du = t ²/864 dt. Then

[tex]P(T)=1-\displaystyle\int_0^T f(t)\,\mathrm dt=1-\displaystyle864\left(1.1574\times10^{-3}\right)\int_0^{\frac{T^3}{2592}}e^{-u}\,\mathrm du[/tex]

The probability that a 12 hour surgery is successful is P (12), so letting T = 12 gives

[tex]P(12)\approx1-\displaystyle\int_0^{\frac23}e^{-u}\,\mathrm du\approx e^{-\frac23} \approx \boxed{0.5134}[/tex]

What is the surface area of the cylinder shown below? Use 3.14 for π.


A. 502.4 cm2
B. 602.88 cm2
C. 785 cm2
D. 602.4 cm2

Answers

it is C

Step-by-step explanation:

i did the test

Answer:

The answer is actually B.

Step-by-step explanation:

I have an actual explanation to this! But I don't like dealing with pdfs, also typing it out will be a lot. Ik I am late, but to whomever else needs help that's the answer! Glad to help:)

Give the equation of the circle centered at the origin and passing through the point -7 0

Answers

Answer: 7.0 because you add 10 to - 3 it makes7.0

Step-by-step explanation:

I attached the question please take a look

Answers

Answer:

e

Step-by-step explanation:

beishdhsjsvsudjdnbdhdjrjdxbxbudsndnbhhxhxbdhddbdbd

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