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
Leya [2.2K]
3 years ago
14

Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k​

Mathematics
1 answer:
masha68 [24]3 years ago
6 0

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

2

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

2

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

2

−2k−4k+12

D=k^2-6k+13D=k

2

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

You might be interested in
Eli wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.00. How much is Company A charging per
Komok [63]

Answer:

Therefore, Company B is offering the lowest price/lb at $12.73/lb.

So, Company A's price / lb = ($32.50/2.5lbs) = $13.00/lb

Step-by-step explanation:

To determine price per lb, divide dollar amount by lbs.

- Company A sells 2 1/2lbs (2.5lbs) for $32.50

- Company B sells 2 3/4lbs (2.75lbs) for $35.00

And, Company B's price / lb = ($35.00/2.75lbs) = $12.73/lb

8 0
3 years ago
DUE IN 10 MINUTES!! PLEASE ANSWER THESE QUESTIONS BELOW. 100 POINTS!!
expeople1 [14]

Answer:

<u>Here is ur answer </u><u>:</u>

1. Probability of composing music for a movie is 1

2. To choose the group in 11 th grade , choosing the subject in which it's more probable to score high marks .

3. To decide whether to go out in rain , the probability of getting cold is more than enjoying the rain .

4. Sorry i don't know

Hope the others will help you !!

8 0
2 years ago
Which of the following shows how the distributive property can be used to find -22(1.5)?
vampirchik [111]

Answer:

the last one

Step-by-step explanation:

4 0
3 years ago
Solve for x. 4+3/5(15+2x)=25
erik [133]
If you would like to solve 4 + 3/5 * (15 + 2x) = 25 for x, you can do this using the following steps:

4 + 3/5 * (15 + 2x) = 25
3/5 * (15 + 2x) = 25 - 4
9 + 6/5 * x = 21
6/5 * x = 21 - 9
6/5 * x = 12        /*5/6
x = 12 * 5/6
x = 10

The correct result would be x = 10.
6 0
3 years ago
The LaSalle high school senior class raised funds for an end of the year cruise getaway. The city gave them a special package fo
makkiz [27]

Answer:

41 students

Step-by-step explanation:

(16,600-1500)/367

7 0
3 years ago
Other questions:
  • Why is the gcf of two numbers is sometimes one
    14·1 answer
  • Solve the compound inequality. NEED NOW.
    13·2 answers
  • If x/5+6=-14 then x equals
    12·1 answer
  • Dylan’s essential (fixed) expenses are $900 per month, his essential (flexible) expenses are $400 per month, and his non-essenti
    14·2 answers
  • Writ the equation included in the same st of related facts as 6×8=48
    15·1 answer
  • sarah thinks of a positive number she calculates that the square of the number is 256 what is the square rootof the number​
    12·1 answer
  • Jane moved from a house with 72 square feet of closet space to an apartment with 44.64 square feet of closet space. What is the
    14·1 answer
  • How many games did you bowl? does this question a statistical question. and why
    12·1 answer
  • Find the selling price of a book with an original price of $49.95 and a 5% tax rate.please be specific on how the answer is the
    6·1 answer
  • Determine the perimeter of a triangle with sides that measure 16.2 inches, 10.04 inches and 12.2 inches.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!