I have a quadratic equation, bx2+2ax+b=0, with a&gt;b&gt;0. I can solve this as followings,x+=−a+a2−b2b,x−=−a−a2−b2b,In my text book, an inequality equation, x{+}2&lt;1&lt;x{−}2, is written with the solution, but I cannot derive the equation. If you can, please teach me the derivation.

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I have a quadratic equation, bx2+2ax+b=0, with a&amp;gt;b&amp;gt;0. I can solve this as followings,x+=−a+a2−b2b,x−=−a−a2−b2b,In my text book, an inequality equation, x{+}2&amp;lt;1&amp;lt;x{−}2, is written with the solution, but I cannot derive the equation. If you can, please teach me the derivation.

Lesly Fernandez · Accepted Answer

Alejandra Hanna · Accepted Answer

Step 1From bx2+2ax+b=0, we can compute the discriminant, of which 4(a2−b2)&amp;gt;0, and we conclude that there are two distinct roots. Furthermore since a&amp;gt;0, b&amp;gt;0, the roots must be negative.Hence x−&amp;lt;x+&amp;lt;0Also,x2+2ab+1=0From the constant term,we can conclude that x+x−=1hence x−&amp;lt;−1&amp;lt;x+&amp;lt;0Hence, we must have x+2&amp;lt;1&amp;lt;x−2

I have a quadratic equation, \(\displaystyle{b}{x}^{{{2}}}+{2}{a}{x}+{b}={0}\), with

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