Solve Quadratic Equation for n^2-3n-4=0

Publish date: 2024-07-03
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Solve the quadratic:

n2-3n-4 = 0

Set up the a, b, and c values:

a = 1, b = -3, c = -4

Quadratic Formula
n  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(-3)

-b = 3

Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = -32 - 4 x 1 x -4

Δ = 9 - -16

Δ = 25 <--- Discriminant

Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(25)

√Δ = 5

-b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = 3 + 5

Numerator 1 = 8

-b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = 3 - 5

Numerator 2 = -2

Calculate 2a

Denominator = 2 * a

Denominator = 2 * 1

Denominator = 2

Find Solutions
Solution 1  =  Numerator 1
  Denominator

Solution 1  =  8
  2

Solution 1 = 4

Solution 2
Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -2
  2

Solution 2 = -1

Solution Set

(Solution 1, Solution 2) = (4, -1)

Prove our first answer

(4)2 - 3(4) - 4 ? 0

(16) - 124 ? 0

16 - 124 ? 0

0 = 0

Prove our second answer

(-1)2 - 3(-1) - 4 ? 0

(1) + 34 ? 0

1 + 34 ? 0

0 = 0

Final Answer

(Solution 1, Solution 2) = (4, -1)

You have 1 free calculations remaining


What is the Answer?

(Solution 1, Solution 2) = (4, -1)

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + 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.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora 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.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

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