1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dem82 [27]
3 years ago
6

Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial

Mathematics
1 answer:
Mariulka [41]3 years ago
7 0

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

You might be interested in
PLEASE HELP
lubasha [3.4K]

Answer:

(a+b)^2+(a-b)^2=2(a^2+b^2)

expanding:

a² + 2ab + b² + a² -2ab + b² = 2a² + 2b²

2a² + 2b² = 2a² + 2b²

7 0
3 years ago
Read 2 more answers
Can someone please help me?! Marking Brainliest!!!!!
irga5000 [103]

Answer:

5\sqrt{2}

Step-by-step explanation:

The formula for the length of a vector/line in your case.

L = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{[4 - (-1)]^2 + [2 -(-3)]^2} = \sqrt{5^2 + 5^2} = \sqrt{50} = 5\sqrt{2}

3 0
3 years ago
Read 2 more answers
Help PLEASE I need help on this question ASAP!!!!
loris [4]

Answer:

$8

Step-by-step explanation:

14 - 6 = 8

3 0
3 years ago
Read 2 more answers
F(x)=x^(2)+3x+4 is this quadratic, linear, or neither
goblinko [34]
Quadratic
you’re welcome
8 0
2 years ago
If Kevin wants a 90 average in math after 5 tests and his first 4 tests are 76, 92, 89 and 97 what does he need on the fifth tes
Keith_Richards [23]
You need to understand that you're solving for the average, which you already know: 90. Since you know the values of the first three exams, and you know what your final value needs to be, just set up the problem like you would any time you're averaging something.
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Oscar rides his skateboard 5/8 mile in 1/4 hour How fast in a mile per hour does he ride his skateboard
    9·2 answers
  • Solve the system using elimination.<br>3x – 3y = 24<br>2x + 2y = 4<br>The solution is |​
    9·1 answer
  • How can you tell if a number is divisible by 4?
    13·1 answer
  • Given the equation StartFraction 2 x + 2 Over y EndFraction = 4 w + 2 what is the value of x?
    7·2 answers
  • Bill Bob has 2 candy but Jonny to 1 alawy. how much candy does bill Bob have left?​
    6·2 answers
  • Simplify the following expression:
    5·1 answer
  • Which of the following terms correctly describe the figure given below
    15·1 answer
  • How many more pieces of mail were handled by the United States Postal Service in 199519951995 than in 196519651965?
    5·1 answer
  • An investor has an account with stock from two different companies. Last year, her
    10·1 answer
  • No Links!! A vinyl record has a circumference of 78.5 cm. What is its area? Use 3.14 for pi and round to the nearest square cm.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!