MHB POTW Director
- Feb 14, 2012
For what values of b do the equation \(\displaystyle 1988x^2+bx+8891=0\) and \(\displaystyle 8891x^2+bx+1988=0\) have a common root?
One of the implied conditions of saying a problem is "easy" is to get it correct. You seem to be in a hurry often when you are posting. We really encourage our users to take a few minutes for every post so we have a higher "post:content" ratio than most forums. It also helps cut down on mistakes and is more efficient for communicating. The same thing goes for formatting equations in Latex - it looks more professional and is easier for others to read. In general, making quality posts is a sign of respect to those who take time to read them. Everything you post is read by multiple people believe it or notI got the numbers wrong in my mind!!!
There is another solution method:
We are given:
(1) \(\displaystyle 1988x^2+bx+8891=0\)
(2) \(\displaystyle 8891x^2+bx+1988=0\)
We can eliminate $x^2$ from both to get:
(3) \(\displaystyle bx=-(8891 + 1988)=-10879\)
Subtracting (2) one from (1) we get:
\(\displaystyle (1988-8891)x^2+(8891–1988)=0\,\therefore\,x^2=1\, \therefore\,x=\pm1\)
From (3) if $x=1$ then $b=-10879$ and if $x=-1$ then $b=10879$