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(4.) Suppose that f(c) = ax? +br + € is a degree-2 polynomial in Rlz]: Please prove that f(x) is reducible over R if and only if 62 4ac > 0....

Question

(4.) Suppose that f(c) = ax? +br + € is a degree-2 polynomial in Rlz]: Please prove that f(x) is reducible over R if and only if 62 4ac > 0.

(4.) Suppose that f(c) = ax? +br + € is a degree-2 polynomial in Rlz]: Please prove that f(x) is reducible over R if and only if 62 4ac > 0.



Answers

A polynomial $f(x)$ with real coefficients and leading coefficient 1 has the given zero(s) and degree. Express $f(x)$ as a product of linear and quadratic polynomials with real coefficients that are irreducible over $\mathbb{R}$. $0,2,-2-\dot{r}$ degree 4


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