Rational Root-Synthetic Division for x^2+7x+6>=0
Using the rational roots (rational zero) theoremDetermine any roots for x2+7x+6> = 0
Set up the a, b, and c values:
a = 1, b = 7, c = 6
Using the rational roots (rational zero) theorem:Find roots for x2 + 7x + 6≥
Rational roots of a polynomial will be q/p where
q is a factor of the constant term (8805)
and p is a factor of the leading x2 coefficient (1)
Determine our list of p values first:
| Numbers (1 - 1) | 1 ÷ Number List | Factor of p? |
|---|---|---|
| 1 | 1 ÷ 1 = 1 | Y |
Let's determine our list of q values next:
| Numbers (1 - 8805) | 8805 ÷ Number List | Factor of q? |
|---|---|---|
| 1 | 8805 ÷ 1 = 8805 | Y |
| 3 | 8805 ÷ 3 = 2935 | Y |
| 5 | 8805 ÷ 5 = 1761 | Y |
| 15 | 8805 ÷ 15 = 587 | Y |
| 587 | 8805 ÷ 587 = 15 | Y |
| 1761 | 8805 ÷ 1761 = 5 | Y |
| 2935 | 8805 ÷ 2935 = 3 | Y |
| 8805 | 8805 ÷ 8805 = 1 | Y |
Calculate our q ÷ p = r values
| p | q | r = q ÷ p | ƒ(r) = r2 + 7r + 6≥ | ƒ(r) value | -1 x r | ƒ(-r) = r2 + 7r + 6≥ | ƒ(-r) value |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | (1)2 + 7(1) + 6≥ | 8813 | -1 | (-1)2 + 7(-1) + 6≥ | 8799 |
| 1 | 3 | 3 | (3)2 + 7(3) + 6≥ | 8835 | -3 | (-3)2 + 7(-3) + 6≥ | 8793 |
| 1 | 5 | 5 | (5)2 + 7(5) + 6≥ | 8865 | -5 | (-5)2 + 7(-5) + 6≥ | 8795 |
| 1 | 15 | 15 | (15)2 + 7(15) + 6≥ | 9135 | -15 | (-15)2 + 7(-15) + 6≥ | 8925 |
| 1 | 587 | 587 | (587)2 + 7(587) + 6≥ | 357483 | -587 | (-587)2 + 7(-587) + 6≥ | 349265 |
| 1 | 1761 | 1761 | (1761)2 + 7(1761) + 6≥ | 3122253 | -1761 | (-1761)2 + 7(-1761) + 6≥ | 3097599 |
| 1 | 2935 | 2935 | (2935)2 + 7(2935) + 6≥ | 8643575 | -2935 | (-2935)2 + 7(-2935) + 6≥ | 8602485 |
| 1 | 8805 | 8805 | (8805)2 + 7(8805) + 6≥ | 77598465 | -8805 | (-8805)2 + 7(-8805) + 6≥ | 77475195 |
Real Roots → ƒ(r) = 0
Root List = {}These are the root(s) using direct substitution.
Below is a link using synthetic division
Click here to see the synthetic division for our polynomial using our root of
Final Answer
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
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