The polynomial x^2-6x+12 in mathbb{Q}[x] is | vedclass

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(A) To determine if the polynomial $f(x) = x^2-6x+12$ is reducible over $\mathbb{Q}$,we check for its roots using the quadratic formula $x = \frac{-b

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irreducible over $\mathbb{Q}$

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(A) To determine if the polynomial $f(x) = x^2-6x+12$ is reducible over $\mathbb{Q}$,we check for its roots using the quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$.Here,$a=1, b=-6, c=12$.The discriminant is $D = b^2-4ac = (-6)^2 - 4(1)(12) = 36 - 48 = -12$.Since the discriminant $D Because the roots are not in $\mathbb{Q}$,the polynomial cannot be factored into linear factors over $\mathbb{Q}$.Since it is a quadratic polynomial with no roots in $\mathbb{Q}$,it is irreducible over $\mathbb{Q}$.

The polynomial $x^2-6x+12 \in \mathbb{Q}[x]$ is

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