MATH: Is this logic correct?

Ask Your Question

MATH: Is this logic correct?



Hi let's say we have a quadratic equation x²-5x+6=0 

To find the value of x we could factorise it to (x-2)(x-3)=0 

So what I was always taught is after you factorise it, you set each one of them to 0, like: 

x-2=0, or x-3=0 
x=2 or x=3. 

I just want to know why we set them =0? I thought it's because logically, for the expression to =0, one of them must be 0, because any number multiplied by 0 is 0. For example, 6(0)=0 

I also thought of this for equations like (x-56)/48=0. To find the value of x, set the (x-56) =0. Because logically, for the fraction to =0, the numerator should be 0. For example 0/6 is =0. The denominator can't be 0 because then the fraction would be undefined. 

Thanks! Just want to know how it works, I was only taught the techniques



Answer this Question:

Close

Close

Posted Answers:

Quadratic Equation x²-5x+6=0 
Solution:
For solution we have to choose 2 numbers whose multiplication is 6 and addition is -5
It is very clearly known the numbers are -3 and -2
So x²-3x-2x+6=0
x(x-3)-2(x-3)=0
(x-3)(x-2)=0
To get the value of x we can take x-3=0 Or x-2=0
So x=3 Or x=2