Question

Form a polynomial whose zeros and degree are given

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

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

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

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

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

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

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

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

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