Why do you factor quadratic equations?

Question

Eva Abramson · Accepted Answer

Because it tells you what the roots of the equation are, i.e. where #ax^2+bx+c=0#, which is often a useful thing to know.

Because it tells you what the roots of the equation are, i.e. where #ax^2+bx+c=0#, which is often a useful thing to know. Think of it backwards - start by knowing that the quantity #x# is zero in two places, #A# and #B#. Then two equations describing #x# are #x-A=0# and #x-B=0#. Multiply them together: #(x-A)(x-B)=0# This is a factored quadratic equation. Multiply out to get the unfactored equation: #x^2-(A+B)x+AB=0# So when you are presented with a quadratic equation, you know that the coefficient of the #x# term is the negative of the sum of the two roots and the constant coefficient is the product of them. This knowledge is usually a help in seeing if you can easily factor a quadratic. For example: #x^2-11x+30=0# Now we want two numbers that add to +11 and multiply to 30; the answers are 5 and 6, we see after trying a few, so it factors as #(x-5)(x-6)=0#.

Hazel Anglin · Answer

By factorising first and then applying the multiplication property of zero, we can solve a quadratic equation.

One of the properties of #0# is that : "Anything multiplied by #0# is equal to #0#" So, if we have an equation where: #a xx b xx cxx d xx e =0#, then because of the multiplication property of #0#, we will know that at least one of the factors being multiplied must be equal to #0#. Since we can't know which one is the #0#, we consider each in turn being #0#. #:. a =0" or " b=0" or " c=0" "or" " d=0" "o r" " e=0# However, this is only true for FACTORS. So to apply this concept in solving a quadratic (or cubic, quartic, etc) equation, start by factorising to find the factors. Then let each factor be equal to #0# and solve to find the possible values of the variable. #x^2+5x=6" "larr# of no help in this form: #x^2+5x-6=0" "larr# make it equal to #0# #(x+6)(x-1)=0" "larr# two factors multiply to give #0# Let each be equal to #0# If #x+6=0" "rarr x =-6# If #x-1=0" "rarr x =1# By factorising first and then applying the multiplication property of zero, we can solve the quadratic equation.

Jace Anderson · Answer

undefined Quadratic equations are factored to find their roots or solutions, which are the values of the variable that satisfy the equation. Factoring helps simplify the equation and makes it easier to solve for the variable. It also helps identify patterns and relationships between the coefficients and roots of the equation. Additionally, factoring quadratic equations is essential for graphing them accurately and understanding their behavior.