If $4x^{2}+Bx+9=(2x+C)^{2}$ for all real values of... | Free GMAT Practice Question | GMAT Panda

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If 4 x^{2} + B x + 9 = (2 x + C)^{2} for all real values of x, where B and C are positive constants, what is the value of B ?

Explanation	Calculations	Help
$We expand the expression on the right side to compare like terms.$	$4 x^{2} + B x + 9 = 4 x^{2} + 4 C x + C^{2}$	Theory & Tactics Method Card EQUA2-A Click to view full details
$We match the coefficient of x on both sides.$	$B = 4 C$
$We match the constant term on both sides.$	$C^{2} = 9$
$Since C is positive, we take the positive square root.$	$C = 3$
$We substitute C = 3 into B = 4 C .$	$B = 4 \times 3$
$We simplify to find the value of B .$	$B = 12$

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C

If 4 x^{2} + B x + 9 = (2 x + C)^{2} for all real values of x, where B and C are positive constants, what is the value of B ?

Explanation	Calculations	Help
$We expand the expression on the right side to compare like terms.$	$4 x^{2} + B x + 9 = 4 x^{2} + 4 C x + C^{2}$	Theory & Tactics Method Card EQUA2-A Click to view full details
$We match the coefficient of x on both sides.$	$B = 4 C$
$We match the constant term on both sides.$	$C^{2} = 9$
$Since C is positive, we take the positive square root.$	$C = 3$
$We substitute C = 3 into B = 4 C .$	$B = 4 \times 3$
$We simplify to find the value of B .$	$B = 12$

Scroll horizontally to view all columns

C