QuestionEquations Points: 0 of 1
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1 , and roots of $2-\sqrt{6}, 2+\sqrt{6}$, and $7-i$.
The polynomial function is $\mathrm{P}(\mathrm{x})=$ $\square$ (Simplify your answer.) View an example Get more help

Studdy Solution
Multiply the two quadratic factors to form the polynomial: $$(x^2 - 4x - 2)(x^2 - 14x + 50)$$
Expand the expression: $$= x^2(x^2 - 14x + 50) - 4x(x^2 - 14x + 50) - 2(x^2 - 14x + 50)$$
$$= x^4 - 14x^3 + 50x^2 - 4x^3 + 56x^2 - 200x - 2x^2 + 28x - 100$$
Combine like terms: $$= x^4 - 18x^3 + 104x^2 - 172x - 100$$
The polynomial function is:
$$\mathrm{P}(x) = x^4 - 18x^3 + 104x^2 - 172x - 100$$