Solve Quadratic Equation for 4x^2+11x-3

Solve the quadratic equation
4x²+11x-3

We have our a, b, and c values:
a = 4, b = 11, c = -3

Solve the quadratic equation
4x² + 11x - 3

Quadratic Formula

x =	-b ± √b² - 4ac
	2a

Calculate -b

-b = -(11)
-b = -11

Calculate the discriminant Δ

Δ = b² - 4ac:
Δ = 11² - 4 x 4 x -3
Δ = 121 - -48
Δ = 169 <--- Discriminant
Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(169)
√Δ = 13

-b + Δ:

Numerator 1 = -b + √Δ
Numerator 1 = -11 + 13
Numerator 1 = 2

-b - Δ:

Numerator 2 = -b - √Δ
Numerator 2 = -11 - 13
Numerator 2 = -24

Calculate 2a

Denominator = 2 * a
Denominator = 2 * 4
Denominator = 8

Find Solutions

Solution 1 =	Numerator 1
	Denominator

Solution 1 =	2
	8

Solution 1 = 0.25 or 1/4

Solution 2 =	Numerator 2
	Denominator

Solution 2 =	-24
	8

Solution 2 = -3

Solution Set

(Solution 1, Solution 2) = (0.25, -3)

Prove our first answer

(0.25)² + 11(0.25) - 3 ? 0
(0.0625) + 2.753 ? 0
0.25 + 2.753 ? 0
0 = 0

Prove our second answer

(-3)² + 11(-3) - 3 ? 0
(9) - 333 ? 0
36 - 333 ? 0
0 = 0

(Solution 1, Solution 2) = (0.25, -3)

What is the Answer?

(Solution 1, Solution 2) = (0.25, -3)

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 = ax^{2^{+ 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 square: a technique for converting a quadratic polynomial of the form ax² + 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