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Solve Quadratic Equation for 4x^2+11x-3
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 + √ΔNumerator 1 = -11 + 13
Numerator 1 = 2
-b - Δ:
Numerator 2 = -b - √ΔNumerator 2 = -11 - 13
Numerator 2 = -24
Calculate 2a
Denominator = 2 * aDenominator = 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)
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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 = 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 meetExample calculations for the Quadratic Equations and Inequalities Calculator
Quadratic Equations and Inequalities Calculator Video
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