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Find all values of \(b\) for which the equations \(1988x^2 + bx + 8891 = 0\) and \(8891x^2 + bx + 1988 = 0\) have a common root.

Enter all the possible values of \(b\), separated by commas.

 

Any help would be appreciated laugh

 Nov 29, 2021
 #1
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-2

The possible values of b are 17675308 and -17675308.

 Nov 29, 2021
 #2
avatar+333 
+9

Can you please show how you got this answer Guest?

abcdefghijklmnopqrst  Nov 29, 2021
 #3
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If the two equations have a common root you can equate them (the two equations) to find the two values of x for which it holds (the bx terms cancel out).

 

Substitute each value of x into either equation and solve for b.  

 

You should find two values (though not 17675308 or -17675308 according to my calculations).

 Nov 29, 2021
edited by Alan  Nov 29, 2021
 #4
avatar+333 
+10

Thanks Alan!

abcdefghijklmnopqrst  Nov 29, 2021
 #5
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0

Also, note that \(ax^2+bx+c\) has the reciprocal of the roots of \(cx^2+bx+a\)

 Dec 4, 2021

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