Question

Find all zeros of the polynomial \[(2{x^4} - 9{x^3} + 5{x^2} + 3x - 1)\] of two of its zeroes are \[(2 + \sqrt 3 )\]and \[(2 - \sqrt 3 )\]

Answer 1

Hint: Polynomials are the algebraic expressions that consist of variables of coefficients. Variables are also sometimes called indeterminate; we can perform arithmetic operations. Such as addition subtraction, Multiplication, and also \[ + ve\] integer exponents for polynomial exp. But not division by variable.
Polynomials appear in many areas of maths and science forex. They are used to form polynomial \[e{q^n}\] which encode a wide range of problems form elementary word problems to complicated scientific problems they are used to define polynomial \[fun{c^n}\] which appear in settings ranging from basic chemistry and social science. They are used in calculus and numerical analysis to approximate other functions. In advanced maths.
Polynomials are used to construct polynomial ring and algebraic varieties which are central concepts in algebra and algebraic geometry.

Complete step by step answer:
Since zeros of polynomial are
\[(2 + \sqrt 3 ),(2 - \sqrt 3 )\]
\[(x - 2 - \sqrt 3 ),(x - 2 + \sqrt 3 )\]
\[{(x - 2)^2} - {(\sqrt 3 )^2}\]
\[{x^2} + 4x + 1 = 0\]
Now dividing the polynomial with \[e{q^n}\](1) of that zero’s will be available
\[\]
\[2{x^2} - x - 1 = 0\]
\[2{x^2} - 2x + x - 1 = 0\]
By complete the square method
\[2x(x - 1) - 1(x - 1)\]
\[(x - 1)(2x - 1)\]
\[x = 1\]\[x = - \dfrac{1}{2}\]
Zero’s of polynomial are
\[ = 1, - \dfrac{1}{2},2 + \sqrt 3 ,2 - \sqrt 3 \]

Note:
 For a polynomial, there could be some values of the variables for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes they are also referred to as roots of the polynomial