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gizmo_the_mogwai [7]
3 years ago
11

Write the quadratic equation in standard form: 2x – 1=-x^2

Mathematics
1 answer:
klasskru [66]3 years ago
3 0

Answer: -x^2-2x-1

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
Christian reads 14 book every 23 week. How many books does Christian read per week?
DedPeter [7]

Answer:

0.609 / week  ( to nearest  thousandth)

or you can state it as 60.9% of a book per week

Step-by-step explanation:

That would be 14/23 =  0.609 / week

6 0
3 years ago
What would be 82% of 50
MrRissso [65]
10% = 5
80% = 40
2% = 1
82% = 41

41
5 0
3 years ago
Read 2 more answers
Which would be considered assets? Check all that apply.
muminat

Answer:

own a guitar

checking account

stocks and bonds

own a motorcycle

Step-by-step explanation:

5 0
3 years ago
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Solve:<br> 1 - 2k += = -3k
MariettaO [177]

Answer:

-1

Step-by-step explanation:

1-2k=-3k

1-2k+2k=-3k+2k

     1=-1k

1/-1=-1k/-1

-1=k

3 0
3 years ago
Read 2 more answers
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