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Find all values of b for which the equations 1988x2+bx+8891=0 and 8891x2+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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The possible values of b are 17675308 and -17675308.

 Nov 29, 2021
 #2
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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
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Thanks Alan!

abcdefghijklmnopqrst  Nov 29, 2021
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Also, note that ax2+bx+c has the reciprocal of the roots of cx2+bx+a

 Dec 4, 2021

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