I am confused about the roots and how they can be used to construct the original quadratic equation.
If I am given the roots of the quadratic equations as $2$ and $3$ I can generate the original equation as $(x-2)(x-3)=0$. Is this right?
Now Let's say the equation is $ax^2+bx+c=0$ and the roots for this equation are P and Q..
So shouldn't the quadratic equation be obtained as $(x-P)(x-Q)=0$, instead in the texts it's mentioned as "$a(x-P)(x-Q)=0$"
Isnt the coefficient of $x^2$ taken care of while finding the roots?why should we multiply it again?