If $x^2+bx+5=(x+c)^2$ for all numbers $x$ , where $b$ and $c$ are positive constants, what is the value of $b$ ?

Correct answer marked below

\sqrt{5}

\sqrt{10}

2 \sqrt{5}

Correct

2 \sqrt{10}

10

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What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

If x2+bx+5=(x+c)2x^2+bx+5=(x+c)^2x2+bx+5=(x+c)2 for all numbers xxx, where bbb and ccc are positive constants, what is the value of bbb?