If x^2+b x+5=(x+c)^2 for all numbers x, where b and c...

Question

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

GMAT Panda · Accepted Answer

2sqrt(5) We expand the right-hand side to compare coefficients. x^2+b x+5 = x^2 + 2 c x + c^2 We match the coefficient of x on both sides. b = 2 c We match the constant term on both sides. c^2 = 5 Since c is positive, we take the positive square root. c = sqrt(5) We substitute c = sqrt(5) into b = 2 c. b = 2 sqrt(5)

Explanation	Calculations	Help
$We expand the right-hand side to compare coefficients.$	$x^{2} + b x + 5 = x^{2} + 2 c x + c^{2}$
$We match the coefficient of x on both sides.$	$b = 2 c$
$We match the constant term on both sides.$	$c^{2} = 5$
$Since c is positive, we take the positive square root.$	$c = 5$
$We substitute c = 5 into b = 2 c .$	$b = 2 \times 5$

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