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4 years ago

Prove that the function f(x) = x 3 + x 2 + 6x + 1 has one and only one real root.

1 answer:

6 0

F(0)=1. When x>0 f(x)>0 because there are no negative coefficients.
f(-1)=-5, so there is a sign change between x=-1 and 0, implying there is one root between these limits.
When x<-1, x³+x²<0 and 6x<0 and so f(x)<0. Therefore there is only one real root.

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12x - 3≤ 59 AND 6x +4> -2

polet [3.4K]

The value of linear Equations and Inequalities x is $5.16\geq x > -1$

linear Equations and Inequalities:

A linear equation is an equation of a straight line where the power of the variable is 1. It is expressed as ax + b = 0, where x is the variable and a and b are integers. Inequality is a statement of comparison between two expressions. Linear Inequations are two expressions where their values are compared by the inequality symbols such as <, >, ≤ or ≥. One variable linear equations and Inequations have only one solution or one root. Examples of one variable linear equations and inequations are x = 4, 2a + 3 = 9, 3x < 2 , 4y - 5 > 6. etc

Method :

For solving a linear equation or inequality having only one variable, the following steps are followed, while still balancing the equation.

Add or subtract like terms

Isolate the variable

Transpose or eliminate the terms

Verify the answer.

Solution :

$12x - 3\leq 59\\12x\leq 59+3\\12x\leq 62\\x\leq \frac{62}{12} \\x\leq \frac{31}{6} \\x\leq 5.16\\\\\\6x +4 > -2\\6x > -2-4\\6x > -6\\x > -1\\\\5.16\geq x > -1$

The value of linear Equations and Inequalities x is $5.16\geq x > -1$

For more details: brainly.com/question/11897796

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7 0

2 years ago

Find the circumference.<br> Use 3.14 for t.<br> r= 2 m<br> C = [?] m<br> C=Td

shusha [124]

Answer:

12.56 m

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

C = 2 * (3.14) * 2

C =12.56

5 0

3 years ago

Read 2 more answers

Help me please. I’ll mark brainliest

Dvinal [7]

Answer:

I don't really understand this question

But if it's asking you to switch,

1. r = 2.5

2. r = 12

3. d = 34

6 0

3 years ago

Rita has a rope 5 m long. She cuts it into 2 pieces of length 2 m 30 cm and 1 m 65 cm.

Diano4ka-milaya [45]

Answer:

3m 95cm

Step-by-step explanation:

its... simple math? i added 2 and 1; and 30 and 65?

6 0

3 years ago

find the side lengths of each triangle. I can't figure out the formula. awnsers with work would be most helpful. Im having most

34kurt

18. (if you needed it)

The triangle is an equilateral triangle, it has 3 congruent/equal side lengths and 3 congruent angles.

To find "z", you can set the sides equal to each other (you can just do two sides since they are all suppose to be the same lengths)

z + 5 = 4z - 4 Subtract z on both sides

5 = 3z - 4 Add 4 on both sides

9 = 3z Divide 3 on both sides

3 = z

Plug this into one of the sides

z + 5

3 + 5 = 8 Each side is 8

[proof]

z + 5

3 + 5 = 8

4z - 4

4(3) - 4

12 - 4 = 8

3z - 1

3(3) - 1

9 - 1 = 8

19. This is an isosceles triangle, which is a triangle that has 2 congruent sides and 2 congruent angles. (The red tick marks shows that the sides are the same/equal)

Since the 2 sides are the same length, you can set them equal to each other to find "x":

2x + 6.8 = 8x + 1.4 Subtract 2x on both sides

6.8 = 6x + 1.4 Subtract 1.4 on both sides

5.4 = 6x Divide 6 on both sides

0.9 = x

Now that you know x, you can find the sides:

2x + 6.8

2(0.9) + 6.8

1.8 + 6.8 = 8.6

8x + 1.4

8(0.9) + 1.4

7.2 + 1.4 = 8.6

The two side lengths are 8.6

5 0

4 years ago