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- Feb 14, 2012
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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?
\(\displaystyle 1988x^2+bx+8891=0=8891x^2+bx+1988\)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?
Thanks for participating, mathmaniac but hey, we're asked to solve for b instead...\(\displaystyle 1988x^2+bx+8891=0=8891x^2+bx+1988\)
\(\displaystyle (8891-1988)x^2-(8891-1988)=0\)
\(\displaystyle x^2=1\)
So x=1
Check your arithmetic...you have the correct expression, you just added incorrectly....
b=-(8891+1988)=-9089
One of the implied conditions of saying a problem is "easy" is to get it correct.I 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:
\(\displaystyle 8891(1988x^2+bx+8891)–1988(8891x^2+bx+1988)=0\)
Or:
\(\displaystyle bx(8891-1988)=1988^2-8891^2\)
(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 $b=10879$