Advantages and Disadvantages of the 4 Methods of Solving Quadratic Equations

OutlineOutline

FactoringFactoring Square Root PropertySquare Root Property Completing the SquareCompleting the Square Quadratic FormulaQuadratic Formula Advantages Advantages Disadvantages Disadvantages SummarySummary

FactoringFactoring

xx22 + 5 + 5xx + 6 = 0 + 6 = 0

((xx + 2)( + 2)(xx + 3) = 0 + 3) = 0

xx + 2 = 0 or + 2 = 0 or xx + 3 = 0 + 3 = 0

xx = -2 or = -2 or xx = -3 = -3

The Square Root PropertyThe Square Root Property

55xx22 = 125 = 125

xx22 = 25 = 25 Divide both sides by 5 to isolate Divide both sides by 5 to isolate xx22

xx = ± = ± √√25 25 Apply the square root propertyApply the square root property

xx = ± 5 = ± 5 SimplifySimplify

Completing the SquareCompleting the Square

xx22 + 6 + 6xx − 7 = 0 − 7 = 0xx22 + 6 + 6xx = 7 = 7 Add 7 to both sidesAdd 7 to both sidesxx22 + 6 + 6xx + 9 = 7 + 9 + 9 = 7 + 9 Add (b/2)Add (b/2)2 2 to both sidesto both sides((xx + 3) + 3)2 2 = 16 = 16 Factor the left sideFactor the left sideUse the Use the Square Root PropertySquare Root Property to complete the solution to complete the solutionxx + 3 = ±4 + 3 = ±4xx = -7, 1 = -7, 1

For aFor axx22 + b + bxx + c = 0, the + c = 0, the value of value of xx is given by: is given by:

SolveSolve: 3: 3xx22 + 2 + 2xx + 1 = 0 + 1 = 0

The Quadratic FormulaThe Quadratic Formula

AdvantagesAdvantages

MethodMethod AdvantagesAdvantages

FactoringFactoring Usually the fastest methodUsually the fastest method

Square Root PropertySquare Root Property Simplest way to solve equations of Simplest way to solve equations of the form (athe form (axx +b) +b)22 = c = c

Completing the SquareCompleting the Square Can always be usedCan always be used

Quadratic FormulaQuadratic Formula Can always be usedCan always be used

DisadvantagesDisadvantagesMethodMethod DisadvantagesDisadvantages

FactoringFactoring Not all polynomials are factorable or Not all polynomials are factorable or they are difficult to factorthey are difficult to factor

Square Root PropertySquare Root Property Few quadratic equations are given in Few quadratic equations are given in the form (athe form (axx +b) +b)22 = c = c

Completing the SquareCompleting the SquareRequires more steps that take time Requires more steps that take time

and are more difficult than other and are more difficult than other methodsmethods

Quadratic FormulaQuadratic Formula More difficult because of the square More difficult because of the square root but calculators can simplify its useroot but calculators can simplify its use

SummarySummary

1.1. Try factoring Try factoring firstfirst because it is easier. because it is easier.2.2. Completing the Square and the Quadratic Completing the Square and the Quadratic

Formula can Formula can alwaysalways be used but they are a be used but they are a bit more difficult.bit more difficult.

3.3. If the equation is in the form If the equation is in the form (a(axx + b) + b)22 = c = c, use , use the square root property.the square root property.