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Arada [10]
3 years ago
13

Form a polynomial whose zeros and degree are given

Mathematics
1 answer:
KonstantinChe [14]3 years ago
6 0

Question:

Form a polynomial whose zero and degree are given .zeros: 3,multiplicity 1 ;1,multiplicity 2 ; degree 3 ?

Answer:

The polynomial is f(x) =  (x^3  - 5x^2  -5x +3)

Step-by-step explanation:

Given:

Zeros = 3,  Multiplicity: 1

Zeros = 1 ,Multiplicity: 2

Degree   : 3

To Find:

The polynomial = ?

Solution:

Let f(x) be the required polynomial

Then

f(x) = (x -3)^1 . (x- 1)^2...................(1)

By using(a-b)^2 =a^2 +b^2-2ab

Equation(1) becomes

f(x) = (x -3)^1\cdot(x^2 +1^2-2(1)(x))

f(x) = (x -3) \cdot (x^2 +1-2x)

f(x) = x (x^2 +1-2x) - 3(x^2 +1-2x)

f(x) =  (x^3 +x-2x^2) - (3x^2 +3-6x)

f(x) =  (x^3 +x-2x^2 - 3x^2 +3-6x)

f(x) =  (x^3  - 3x^2-2x^2 +x -6x +3)

f(x) =  (x^3  - 5x^2  -5x +3)

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