What is greater 4 yards or 13 feet?

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

The angles in a triangle are in the ratio 1:2:3. Show that this triangle is a right-angled triangle. The hypotenuse of the trian

natita [175]

Answer:

see explanation

Step-by-step explanation:

(a)

Sum the parts of the ratio , 1 + 2 + 3 = 6 parts

Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Since there is an angle of 90° then the triangle is right.

(b)

The shortest side is the side opposite the smallest angle of 30°

Using the sine ratio and the exact value

sin30° = $\frac{1}{2}$ , then

sin30° = $\frac{opp}{hyp}$ = $\frac{opp}{19}$ = $\frac{1}{2}$ ( cross- multiply )

2 opp = 19 ( divide both sides by 2 )

opp = 9,5

Shortest side in the triangle is 9.5 cm

6 0

2 years ago

Use Midpoint and Slope Formulas to complete the tables below.1. Find the midpoint of RP, given the coordinates R (5, 8) and P (3

poizon [28]

The midpoint formula for a segment is:

$x_m,y_{_m}=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2}$

apply to points R and P

$\begin{gathered} x_m,y_m=\frac{(5+3)}{2},\frac{(8+6)}{2} \\ x_m,y_m=\frac{8}{2},\frac{14}{2} \\ x_m,y_m=(4,7) \end{gathered}$

using the definition of slope find the slope of the segment

$m=\frac{y_2-y_1}{x_2-x_1}$

apply to points R and P

$\begin{gathered} m=\frac{8-6}{5-3} \\ m=\frac{2}{2} \\ m=1 \end{gathered}$

to lines are parallel when the slopes are the same

$\mleft\Vert m=1\mright?$

two lines are perpendicular when the product of the slopes is equal to -1

$\begin{gathered} m\cdot\perp m=-1 \\ 1\cdot\perp m=-1 \\ \perp m=-\frac{1}{1} \\ \perp m=-1 \end{gathered}$

7 0

1 year ago

10 percent increase of $29000 over 5 years,will give brainly is urgent

Tema [17]

Answer:

$43,500

Step-by-step explanation:

10 percent increase of $29,000

10% = 0.10

29,000*0.10 = 2,900

So 2,900 a year

so 2,900*5 = 14,500

Then add

29,000+14,500 = 43,500

8 0

3 years ago

A store sells 4 cans of fruit cocktail for $9. How much would it cost you to buy 3 cans of fruit cocktail?

horsena [70]

Answer:

9:4=2.25 3x2.25=6.75 i think lol

6 0

3 years ago

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