Question #a0d7b

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Oct 8, 2017

The factors of the equation are #(x-5)(x+3)#

Explanation:

As we can see , #x^2-2x-15=0# is a quadratic equation, therefore it must have two roots.

There is a basic way of finding factors of an quadratic equation.

A general quadratic equation is in the form #ax^2+bx+c=0# .
To factor this equation we need to find two number whose product would be equal to #cxxa# and sum would be equal to #b#. Let's say we did find those two numbers and name them #p# and #q# .
We will then proceed to write our original equation as->

#ax^2+px+qx+c=0#

The next step of the explanation is given below.

Taking your question as an example, we need two numbers whose product is #(-15)# and adds up to #(-2)#
As we know the product of #(-5)# and #3# is #(-15)# , and when we add up #(-5)# and #3# we get #3+(-5)=(-2)#.

Now we write our equation as #x^2-5x+3x-15=0#

As you can see we can take #x# common out of the first two elements and take #3# common form element 3 and 4.

That would give us
#x(x-5)+3(x-5)=0#

Again we can take #(x-5)# common from the above equation and we will be left with
#(x-5)(x*1+3*1)=0#

which is equal to

#(x-5)(x+3)=0#

so, the factors of the equation are #(x-5)(x+3)#

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