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# Any help would be appreciated! Thanks!

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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

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The largest possible value of b is -9.

Oct 17, 2020
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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).

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

!

Oct 17, 2020
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Thanks asinus! You were right!

Guest Oct 18, 2020