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3 years ago

The number 3 is an upper bound for the set of roots of this polynomial

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

3 0

Answer:

True

Step-by-step explanation:

The bottom line from synthetic division is 3, 4, 7, 26. All of these values are positive, indicating that 3 is an upper bound on the roots.

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What are the roots to<br> the equation<br> 2x² + 6x-1=0?

lys-0071 [83]

Answer:

The roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Step-by-step explanation:

The given quadratic equation is 2 x² + 6 x - 1 = 0

This equation is in form of a x² + b x + c = 0

Let the roots of the equation are ( m , n )

Now , sum of roots = $\frac{ - b}{a}$

And products of roots = $\frac{c}{a}$

So, m + n = $\frac{ - 6}{2}$ = - 3

And m × n = $\frac{ - 1}{2}$

Or, (m - n)² = (m + n)² - 4mn

Or, (m - n)² = (-3)² - 4 ( $\frac{ - 1}{2}$ )

Or, (m - n)² = 9 + 2 = 11

I.e m - n = $\sqrt{11}$

Again m + n = - 3 And m - n = $\sqrt{11}$

Solving this two equation

(m + n) + ( m - n) = - 3 + $\sqrt{11}$

I.e 2 m = - 3 + $\sqrt{11}$

Or, m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$

Similarly n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Hence the roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$ Answer

6 0

3 years ago

I need help with finding slopes from two points thank you

otez555 [7]

Answer:

i do believe the answer is 6/7

7 0

3 years ago

Can you please help asap

dybincka [34]

For question 38 it would be C. -38 because -38 - 7 is -45 and -45 divided by 9 is -5.

Question 35 would be B. 4/5 because 80% converted into a decimal is 4/5.

Hope these helped!! :)

7 0

3 years ago

two positive numbers x and y, with the maximum value 4, add up to 5. what is the difference between the maximum and minimum valu

Svetach [21]

Answer:

Step-by-step explanation:

Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...

x²(5-x)³

A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.

The difference between the maximum and minimum is 108-16 = 92.

_____

If you like, you can take the derivative and set it to zero.

f(x) = x²(5 -x)³

f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)

f'(x) = 5x(5-x)²(2-x)

This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.

To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...

f(1) = 1²·4³ = 64

f(2) = 2²·3³ = 108 . . . . product maximum

f(4) = 4²·1³ = 16 . . . . . . product minimum

The difference between the maximum and minimum is 92.

5 0

3 years ago

Write 2.08 three ways

topjm [15]

Answer:

2.080

2.0800

2.08000

Step-by-step explanation:

We can write 2.08 in infinite ways by simply adding zeros.

6 0

3 years ago

Read 2 more answers