MATHEMATICS HIGH SCHOOL

x²-2x+1 let a, b, c be positive integers such that the quadratic equation ax² - bx + c = 0 has two distinct roots in the interval (0,1). Find the smallest possible value of a.

Answers

Answer 1

Answer:

Answer:

The least value of a = 1

Step-by-step explanation:

As it has two distinct roots. According to roll's theorem there should be a point where f'(x)=0

In a quadratic equation ax² + bx + c = 0 the point of maxima or minima is

x = - b/2a

We can find by differentiating it

2ax - b= 0

x = b/2a

So 0 < b/2a < 1

0 < b/a < 2

0 < b < 2a

a > b/2

then, the least value of b = 2 and the least value of a = 1

Related Questions

7000 is 10 times as much as
Help on Question number 14 Determine whether each of the following is the graph of a function.
What is the reflection image of (5, -3) across the line y = -x?
Simplify (6x^2+11x-3) + (2x^2-17x-4)
Find the least number by which 1470 must be divided to get a number which is the perfect square?

A triangle has two sides of lengths 7 and 9. What value could the length of the third side be?

Answers

x - length of the 3rd side

$7+9>x \wedge 7+x>9 \wedge 9+x>7\n x<16 \wedge x>2 \wedge x>-2\n x\in(2,16)$

Solve this inequality: 3p – 16 < 20. A. p < 1/3
B. p < 11/3
C. p < 12
D. p < –12

Answers

If you would like to solve the inequality 3 * p - 16 < 20, you can calculate this using the following steps:

3 * p - 16 < 20
3 * p < 20 + 16
3 * p < 36 /3
p < 36/3
p < 12

The correct result would be C. p < 12.

The solution to the inequality is p < 12.

Option C is the correct answer.

We have,

To solve the inequality 3p - 16 < 20, you can follow these steps:

- Add 16 to both sides of the inequality:

3p - 16 + 16 < 20 + 16

3p < 36

- Divide both sides of the inequality by 3

(since the coefficient of p is 3 and we want to isolate p):

(3p)/3 < 36/3

p < 12

Thus,

The solution to the inequality is p < 12.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ6

Which of the following could not be true for a function?Domain is {2}, Range is {2}
Domain is {2, 3}, Range is {2}
Domain is {2}, Range is {2, 3}
Domain is {2, 3}, Range is {2, 3}

Answers

C. hope this helps :::)

Answer:

I agree with C

Step-by-step explanation:

Log2/3 9/4=x+3 ????????????????

Answers

$log_{ (2)/(3) } (9)/(4) =x+3\n\nlog_{ (2)/(3) }( (2)/(3))^(-2) =x+3\n\n-2=x+3\n\n-x=3+2\n\n-x=5\ /\cdor(-1)\n\nx=-5$

$log_{(2)/(3)}(9)/(4)=x^3\n \n \left((2)/(3)\right)^x+3=(9)/(4)\n \n \left((2)/(3)\right)^(x+3)=\left((2)/(3)\right)^(-2)\n \n x+3=-2\n \n x=-2-3\n \n \boxed{x=-5}$

Alison is saving for retirement. Her company matches what she puts into her 401K in a ratio of 2:3. If she puts in $400 each month, how much in total is put into her 401k each month?A) $200
B) $800
C) $600
D) $1,000

Answers

Answer:

D) $1000

Step-by-step explanation:

Her company is using a ratio of 2:3 of what she is putting into her account. That means that for every two dollars that she puts into her 401K , the put in three dollars.

Therefore, if she puts away $400 each month:

2 : 3

400 : 600

Her company will pay $600 into her 401K.

That gives her a total of:

400 + 600 = $1000

id say B...............

A stop sign is in the shape of a regular octagon with a side length of 8 inches and an apothem of 9.5 inches. What is the area pf the stop sign choices

608 in^2
456 in^2
304 in^2
228 in^2