Mathematics: Apolynomial with rational coefficients has roots 5 and -6i. (the i is an imaginary number not variable). what is the polynomial? with work shown

Apolynomial with rational coefficients has roots

tremainewoodley3030

11.01.2022

The answer is { $x^{3}$ -(5) $x^{2}$ (36)× -(180)

Step-by-step explanation:

A polynomial with rational coefficients has roots 5 and -6i (There i is the

imaginary number not variable )

As we knew that imaginary no comes in pair . This means that if -6i is

one root then the other root will be 6i

So if we assume the lowest polynomial that is possible is given as

{ $x^{3}$ -(sum of all roots) $x^{2}$ +(roots taken two at a time)

-(product of all roots)

{ $x^{3}$ -(5+6i+(-6i)) $x^{2}$ +(5×6i +5×(-6i) +6i×(-6i))

-(5×6i×(-6i))

i^2 = -1

{ $x^{3}$ -(5) $x^{2}$ (36)× -(180)

The general case we assume that the three previous roots and rest roots

a4,a5,a6 ...............an

x^n -(sum of all roots)× $x^{n-1}$ +(roots taken two at a

time) × $x^{n-2}$ - .......................................... (product of all roots)

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