We know that when a quadratic equation ax2+bx+c=0ax2+bx+c=0 has zero discriminant value, then the quadratic equation has only "one root". But why do some mathematician call it "double root" and also that the equation still has two roots, but their roots are double. When we draw the equation in the coordinate plane, we can see that the graph of the equation will just touch the xx-axis at only one point.
The second question is: We know that the sum of the roots of a quadratic equation ax2+bx+c=0ax2+bx+c=0 is −ba. But when the discriminant of that equation is zero, the sum is also −ba. It doesn't make sense. For example, if we have quadratic equation x2+4x+4=0, we can factor it as (x+2)2=0 and so x=−2. Thus, the sum is just −2. But with "sum of the roots" formula, the sum is −4. Which one is correct? Is this the reason we call it double root?
Thanks in advance :)