# Fungrim entry: fc2582

$\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[a {z}^{2} + b z + c\right] = \left\{\frac{-b + \sqrt{{b}^{2} - 4 a c}}{2 a}, \frac{-b - \sqrt{{b}^{2} - 4 a c}}{2 a}\right\}$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0$
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[a {z}^{2} + b z + c\right] = \left\{\frac{-b + \sqrt{{b}^{2} - 4 a c}}{2 a}, \frac{-b - \sqrt{{b}^{2} - 4 a c}}{2 a}\right\}

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0
Definitions:
Fungrim symbol Notation Short description
Zeros$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$ Zeros (roots) of function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Sqrt$\sqrt{z}$ Principal square root
Source code for this entry:
Entry(ID("fc2582"),
Formula(Equal(Zeros(Add(Add(Mul(a, Pow(z, 2)), Mul(b, z)), c), ForElement(z, CC)), Set(Div(Add(Neg(b), Sqrt(Sub(Pow(b, 2), Mul(Mul(4, a), c)))), Mul(2, a)), Div(Sub(Neg(b), Sqrt(Sub(Pow(b, 2), Mul(Mul(4, a), c)))), Mul(2, a))))),
Variables(a, b, c),
Assumptions(And(Element(a, CC), Element(b, CC), Element(c, CC), NotEqual(a, 0))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC