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Ilya [14]
3 years ago
10

What are the zeros of the polynomial function f(x)=x^3-2x^2-8x?

Mathematics
1 answer:
Rashid [163]3 years ago
3 0

Answer: -2, 0, 4

Set the equation equal to zero.

x³ - 2x² - 8x = 0

Factor out x in the equation, since all the terms (x³, -2x², and -8x) are divisible by x. You can check your accuracy using the Distributive Property.

x(x² - 2x - 8) = 0

Factor out the polynomial. To do this, find two numbers that multiply to get the last term, -8, and add together to get the middle term, -2. In this case, those two numbers are -4 and 2 (-4 × 2 = -8 and -4 + 2 = -2). Don't forget about the x that was factored out before!

x(x - 4)(x + 2) = 0

Set each factor equal to zero and solve for x. The factors in the equation are x, (x - 4), and (x + 2).

  • x = 0
  • (x - 4) = 0

        x = 4

  • (x + 2) = 0  

        x = -2

The zeros of the polynomial function are -2, 0, and 4.

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There are three options which are the square roots of 100, and those are C. -10, D. 10, and F. |10|
C: (-10)^2 = -10 * -10 = 100 (- * - = +)
D: 10 * 10 = 100
F: |10| = 10, and 10 * 10 = 100 (these brackets make a negative number positive, and a positive number stays positive)
6 0
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Compute the probability of randomly selecting a three or club.
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2 years ago
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
←<br><br> How many solutions does this linear system have<br> y =<br> x+2<br> 6x - 4y = -10
defon

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

<u>Slope-intercept form</u>

y = mx + b

m ... slope

b ... y-intercept

6x - 4y = -10

6x + 10 = 4y

\frac{6}{4}x + \frac{10}{4} = y

\frac{3}{2}x + \frac{5}{2} = y

If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.

If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.

If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.

We see that lines have different slopes. First line has slope 1 and the other line has slope \frac{3}{2}. So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

8 0
1 year ago
572 cars were parked in a parking garage. The same number of cars was parked on each floor. If there were 4 floors, how many car
tatuchka [14]

Answer:

143 cars on each floor

Step-by-step explanation:

572 / 4 = 143

4 0
2 years ago
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