Question

5x^2 - 17x + 6 = 0Solve by using zero product property. Solve for x

Answer 1

Given:

`5x^2-17x+6=0`

To use the zero product property we have to rearrange the equation so that we can factor out two linear equations such that they give this format: a * b = 0

To start we multiply 5 and 6 to get 30

From here we will find common factors of 30 that they add up to -17.

30:

-1 -30

-2 -15

We stop here because -2 + -15 =-17 and when multiplied they get us +30.

So now:

`5x^2-17x+6=0\Rightarrow5x^2-15x-2x+6=0`

Here is we can start to factor out the equation.

`5x^2-15x-2x+6=0\Rightarrow5x(x-3)-2(x-3)=0`

Since we have two (x-3) we can factor out the 5x and -2 into:

`(5x-2)(x-3)=0`

This is the zero product property and now we have to solve for x.

`5x-2=0\Rightarrow5x=2\Rightarrow x=(2)/(5);\text{ }x-3=0\Rightarrow x=3`

Answer:

`x=(2)/(5)\text{ }and\text{ }x=3`