To calculate: polynomial equation with real coefficients that has roots 0,i \sqrt{3}

Harlen Pritchard

Harlen Pritchard

Answered question

2021-08-01

To calculate: Polynomial equation with real coefficients that has roots 0,i3.

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-08-02Added 92 answers

Formula used:
(a+b)(ab)=a2b2
Calculation:
If the polynomial has real coefficients, then it's imaginary roots occur in conjugate pairs. So, a polynomial with the given root i3 must have another root as i3.
Since each root of the equation corresponds to a factor of the polynomial, also, the roots indicate zeros of that polynomial, thus, the polynomial equation is written as,
(x0)[x(i3)][x(i3]=0
(x)(xi3)(x+i3)=0
Further use arithmetic rule,
(a+b)(ab)=a2b2
Here, a=x,b=i3 and i2=1
Now, the polynomial equation is,
(x)(x2(i3)2)=0
(x)(x2+3)=0
x3+3x=0
Hence, the polynomial equation of given roots 0,i3 is x3+3x=0.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-06Added 2605 answers

Answer is given below (on video)

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