query: Prove $\mathbb{R}[X]/(ax^2 + bx +c) \cong \mathbb{C}$ if $b^2 - 4ac < 0$
positive_passages.docid: 147667
positive_passages.text: Polynomial ring isomorphisms
negative_passages.docid: 29452
negative_passages.text: Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
negative_passages.docid: 12825
negative_passages.text: Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
negative_passages.docid: 114198
negative_passages.text: Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
negative_passages.docid: 30752
negative_passages.text: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
negative_passages.docid: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 43478
negative_passages.text: Prove that: $ m_a + m_b + m_c \le 4R + r $
negative_passages.docid: 5996
negative_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 46831
negative_passages.text: Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
negative_passages.docid: 152693
negative_passages.text: If $C|a$ and $C|b$ then $C|(ax+by)$
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 25258
negative_passages.text: Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
negative_passages.docid: 125164
negative_passages.text: How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
negative_passages.docid: 36996
negative_passages.text: If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
negative_passages.docid: 56612
negative_passages.text: Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
negative_passages.docid: 83337
negative_passages.text: If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$