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Rzqust [24]
3 years ago
9

I need help with my homework

Mathematics
1 answer:
lapo4ka [179]3 years ago
3 0

Answer:

ok tell me the questions

Step-by-step explanation:

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Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0
3 years ago
What is 5 times 5 <br> and also what is 5 plus 5 bc im rly silly
timofeeve [1]

Answer:

5 x 5 = 25 and 5 + 5 = 10

Step-by-step explanation:

You multiply 5 Five times.

So you get 5,10,15,20,25!

The answer is 25

You add 5 two times.

So you get 5 plus 5!

5,6,7,8,9,10!

The answer is 10

Hope this helped!

~Oreo!!

5 0
3 years ago
(-6,1) is a point on the graph of y=g(x)
NNADVOKAT [17]

Answer:

(-7, -4)

(-4, 2)

(-4, 1)

Step-by-step explanation:

We know that the point (-6, 1) belongs to the main function g(x)

The transformation

y = g (x + 1) -5

add 1 to the input variable (x) and subtract 5 to the output variable (y)

So the point in the graph of y = g (x + 1) -5 is

x + 1 =-6\\x = -7

y= 1-5\\y = -4

The point is:  (-7, -4)

The transformation

y = -2g(x -2) +4

subtract two units from the input variable (x), multiply the output variable (y) by -2 and then add 4 units

So the point in the graph of y = -2g(x -2) +4 is

x -2 =-6\\x = -4\\\\y = -2(1)+4\\y = 2

The point is:  (-4, 2)

The transformation

y=g(2x+2)

Multiply the input variable (x) by 2 and then add two units

So the point in the graph of   y=g(2x+2) is

2x +2 =-6\\2x = -8\\x=-4

y=1

The point is:  (-4, 1)

3 0
3 years ago
Compute the total cost of the meal to the nearest cent:
sveticcg [70]

Answer:

D. $32.67

Step-by-step explanation:

4 0
3 years ago
The picture shows a circle divided into 8 equal wedges which are rearranged.
slega [8]
I’m pretty sure the answer is 60!!!!
8 0
3 years ago
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