a little quary

[chandra21]

are the quadratic formulas valid for irration coefficients of? Here quadratic formula means, if ax^2+bx+c=0,and m and n are the roots of the above equation then is it m+n=(-b/a) possible a,b are irrations.

 

[HallsofIvy]

The quadratic formula says that the two roots to the quadratic equation \(\displaystyle ax^2+ bx+ c= 0\) are given by \(\displaystyle x_1= \frac{-b+\sqrt{b^2- 4ac}}{2a}\) and \(\displaystyle x_2= \frac{-b- \sqrt{b^2- 4ac}}{2a}\), whether the coefficients are rational or irrational. And, since the square root parts cancel, \(\displaystyle x_1+ x_2= \frac{-b}{2a}+ \frac{-b}{2a}= -\frac{b}{a}\). Again that is true for a, b, and c any numbers, ration, irrational, or even complex (except, of course, for a= 0 when the equation wouldn't really be quadratic).

 

[chandra21]

thats all i want to know. I can't express my feelings to have such great teacher around me. Many many thanks.