If $2v^{2} + b v + 18 = 2(v + t)^{2}$ for all numb... | Free GMAT Practice Question | GMAT Panda

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If 2 v^{2} + b v + 18 = 2 (v + t)^{2} for all numbers v, where b and t are positive constants, what is the value of b ?

Explanation	Calculations	Help
$We expand the right-hand side to compare coefficients.$	$2 v^{2} + b v + 18 = 2 (v^{2} + 2 t v + t^{2}) = 2 v^{2} + 4 t v + 2 t^{2}$	Theory & Tactics Method Card EQUA2-A Click to view full details
$We match the coefficient of v on both sides.$	$b = 4 t$
$We match the constant term on both sides.$	$2 t^{2} = 18$
$Since t is positive, we take the positive square root.$	$t = 3$
$We substitute t = 3 into b = 4 t .$	$b = 4 \times 3 = 12$

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C

If 2 v^{2} + b v + 18 = 2 (v + t)^{2} for all numbers v, where b and t are positive constants, what is the value of b ?

Explanation	Calculations	Help
$We expand the right-hand side to compare coefficients.$	$2 v^{2} + b v + 18 = 2 (v^{2} + 2 t v + t^{2}) = 2 v^{2} + 4 t v + 2 t^{2}$	Theory & Tactics Method Card EQUA2-A Click to view full details
$We match the coefficient of v on both sides.$	$b = 4 t$
$We match the constant term on both sides.$	$2 t^{2} = 18$
$Since t is positive, we take the positive square root.$	$t = 3$
$We substitute t = 3 into b = 4 t .$	$b = 4 \times 3 = 12$

Scroll horizontally to view all columns

C