Solve Quadratic Equation for x^2-x-12=0 ·

19 Jun 2024, 00:00

Solve Quadratic Equation for x^2-x-12=0

Solve the quadratic equation
x2-x-12 = 0

We have our a, b, and c values:
a = 1, b = 1, c = -12

Solve the quadratic equation
x2 + x - 12=

Quadratic Formula

x =	-b ± √b2 - 4ac
	2a

Calculate -b

-b = -(1)
-b = -1

Calculate the discriminant Δ

Δ = b2 - 4ac:
Δ = 12 - 4 x 1 x -12
Δ = 1 - -48
Δ = 49 <--- Discriminant
Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(49)
√Δ = 7

-b + Δ:

Numerator 1 = -b + √Δ
Numerator 1 = -1 + 7
Numerator 1 = 6

-b - Δ:

Numerator 2 = -b - √Δ
Numerator 2 = -1 - 7
Numerator 2 = -8

Calculate 2a

Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2

Find Solutions

Solution 1 =	Numerator 1
	Denominator

Solution 1 =	6
	2

Solution 1 = 3

Solution 2 =	Numerator 2
	Denominator

Solution 2 =	-8
	2

Solution 2 = -4

Solution Set

(Solution 1, Solution 2) = (3, -4)

Prove our first answer

(3)2 + 1(3) - 12 ? 0
(9) + 312 ? 0
9 + 312 ? 0
0 = 0

Prove our second answer

(-4)2 + 1(-4) - 12 ? 0
(16) - 412 ? 0
16 - 412 ? 0
0 = 0

(Solution 1, Solution 2) = (3, -4)

What is the Answer?

(Solution 1, Solution 2) = (3, -4)

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

Solve Quadratic Equation for x^2-x-12=0

We have our a, b, and c values:a = 1, b = 1, c = -12 Solve the quadratic equationx2 + x - 12= (Solution 1, Solution 2) = (3, -4) What is the Answer? (Solution 1, Solution 2) = (3, -4) How does the Quadratic Equations and Inequalities Calculator work?