Question #a0d7b

1 Answer
Oct 8, 2017

The factors of the equation are (x5)(x+3)

Explanation:

As we can see , x22x15=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 ax2+bx+c=0 .
To factor this equation we need to find two number whose product would be equal to c×a 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->

ax2+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 x25x+3x15=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(x5)+3(x5)=0

Again we can take (x5) common from the above equation and we will be left with
(x5)(x1+31)=0

which is equal to

(x5)(x+3)=0

so, the factors of the equation are (x5)(x+3)