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# For what value of 'm' will the roots xone and xtwo of the

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Senior Manager
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For what value of 'm' will the roots xone and xtwo of the [#permalink]  26 Jan 2004, 15:28
For what value of 'm' will the roots xone and xtwo of the quadratic equation
x^2 + x + m = 0 satisfy the relation 9xone + 4xtwo = 26?
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Pls include reasoning along with all answer posts.
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Manager
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We r given that (xone + xtwo)= -1 , (xone * xtwo) = m and (9xone + 4xtwo)= 26, from here I am not able to proceed, hmmmm back to basics, it will be easier from choices, let somebody else try it, Sunniboy the main drawback to my preparation is that I dont have a single GMAT book with me, so presently just browing this site. I am waiting for the books and then the real fun starts.
Director
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X1=-1+sqrt(1-4m)/2 and X2=-1+sqrt(1-4m)/2 ( formula for the roots of square equation), substitute in 9X1+4X2=26 and solve for m, should be -42.
Senior Manager
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easier way to do this would be:

X1+X2 = -1
X1*X2=m

9X1+4X2=26 ---> 5X1 +4(X1+X2) = 26 ----> X1=6, hence X2 = -7
Therefore m = -42
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Manager
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this is good, i didnt know how to proceed and got the idea now.
SVP
Joined: 30 Oct 2003
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got -42 but in a lengthy way

roots of equation x^2+x+m are

( -1+sqrt( 1-4m ) )/2
and
( -1-sqrt( 1-4m ) )/2

9( ( -1+sqrt( 1-4m ) )/2 ) + 4( ( -1-sqrt( 1-4m ) )/2 ) = 26

I get m = -42
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