Algebra-2

1. Recall the conjugate root theorem:

If a polynomial with real - valued coefficients has a complex root , then its conjugate  is also a root of the polynomial.

Given that one root is , then its conjugate  is also a root of the cubic polynomial since the polynomial has real coefficients. Another given root is .

 

2. Write the polynomial in factored form:

If  are the roots of a polynomial, then the polynomial  can be written as , where  is a non - zero real number. For simplicity, we can let .

So, .

 

3. First, multiply the complex conjugate factors:

.

Using the difference of squares formula , where  and , we get .

Expand :

 and

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