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Fungrim entry: fc2582

zeroszC(az2+bz+c)={b+b24ac2a,bb24ac2a}\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:aCandbCandcCanda0a \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
ZeroszerosP(x)f ⁣(x)\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right) Zeros (roots) of function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Sqrtz\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), z, Element(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), Unequal(a, 0))))

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2019-08-21 11:44:15.926409 UTC