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The two solutions of the equation \(x^2+bx+18=0\) are in the ratio of \(2\) to \(1\) for some values of \(b.\) What is the largest possible value of \(b?\)

 Oct 17, 2020
 #1
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The largest possible value of b is -9.

 
 Oct 17, 2020
 #2
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The two solutions of the equation \(x^2+bx+18=0\)  are in the ratio of 2  to 1  for some values of b. What is the largest possible value of b.

 

Hello Guest!

 

\(x=-\frac{b}{2}\pm \sqrt{(\frac{b}{2})^2-18}\\ \ \)

 

b = - 9 :    x1 = 6        x2 = 3       x2 : x1 = 1 : 2

b=    9 :    x1 = - 6      x2 = - 3     x2 : x1 = 1 : 2

The largest possible value of b is 9 (for x1: x2 = 1: 2).

\(b\in \mathbb R\ |b\le-6\sqrt{2}\ and\ 6\sqrt{2}\le b\)

laugh  !

 
 Oct 17, 2020
 #3
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Thanks asinus! You were right! laugh

 
Guest Oct 18, 2020

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