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![If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h"){kind=icon}
27 Oct 2018, 10:27
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If a and b are constants, and the equation \(x^3 +ax^2 +bx = 64\) has precisely one solution for x, what is the value of b?
A) 48
B) 16
C) 24
D) -16
E) -67
A) 48
B) 16
C) 24
D) -16
E) -67
27 Oct 2018, 10:27
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Because if this cubic polynomial has only one root, 4 , then the equation can be written as:
(x - 4)^3 = 0
And then when we expand this we will get :
\(x^3 - 3*4*x^2 + 3*4^2*x - 64 = 0\)
Hence comparing to equation given, we get b = 48
(x - 4)^3 = 0
And then when we expand this we will get :
\(x^3 - 3*4*x^2 + 3*4^2*x - 64 = 0\)
Hence comparing to equation given, we get b = 48
