Solve the quadratic:

w^{2}+3w-108 = 0

a = 1, b = 3, c = -108

w = | -b ± √b^{2} - 4ac |

2a |

-b = -(3)

-b = -3

Δ = b^{2} - 4ac:

Δ = 3^{2} - 4 x 1 x -108

Δ = 9 - -432

Δ = 441 <--- Discriminant

Since Δ > 0, we expect two real roots.

√Δ = √(441)

√Δ = 21

Numerator 1 = -b + √Δ

Numerator 1 = -3 + 21

Numerator 1 = 18

Numerator 2 = -b - √Δ

Numerator 2 = -3 - 21

Numerator 2 = -24

Denominator = 2 * a

Denominator = 2 * 1

Denominator = 2

Solution 1 = | Numerator 1 |

Denominator |

Solution 1 = | 18 |

2 |

Solution 1 = 9

Solution 2 = | Numerator 2 |

Denominator |

Solution 2 = | -24 |

2 |

Solution 2 = -12

(Solution 1, Solution 2) = (9, -12)

(9)^{2} + 3(9) - 108 ? 0

(81) + 27108 ? 0

81 + 27108 ? 0

0 = 0

(-12)^{2} + 3(-12) - 108 ? 0

(144) - 36108 ? 0

144 - 36108 ? 0

0 = 0

(Solution 1, Solution 2) = (9, -12)

(Solution 1, Solution 2) = (9, -12)

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

This calculator has 4 inputs.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

This calculator has 4 inputs.

y = ax^{2 + bx + c(-b ± √b2 - 4ac)/2ah (Axis of Symmetry) = -b/2aThe vertex of a parabola is (h,k) where y = a(x - h)2 + kFor more math formulas, check out our Formula Dossier}

- complete the square
- a technique for converting a quadratic polynomial of the form ax
^{2}+ bx + c to a(x - h)^{2}+ k - equation
- a statement declaring two mathematical expressions are equal
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- intercept
- parabola
- a plane curve which is approximately U-shaped
- quadratic
- Polynomials with a maximum term degree as the second degree
- quadratic equations and inequalities
- rational root
- vertex
- Highest point or where 2 curves meet

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