2022-04-01
A polynomial f(x) with real coefficients and leading coefficient 1 has the given zero and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
7 + 8i; degree 2
user_27qwe
Skilled2022-04-21Added 375 answers
The roots of the polynomial is
Root is imaginary. The imaginary or complex Roots always exist as Complex Conjugates.
This implies, the second root is and the two roots of are
From Factor Theorem, if is root of polynomial then is a factor of the polynomial
Therefore, the polynomial can be written as
Simplify terms.
Simplify each term.
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Combine the opposite terms in .
Simplify each term.
Simplify by adding terms.
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