Question

Form a polynomial whose zeros and degree are given

Zeros: 3, Multiplicity 1;

Multiplicity 2; Degree 3

Answer 1

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)`

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)`