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# If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?  [#permalink]

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21 Jan 2019, 23:48
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:47) correct 32% (02:23) wrong based on 26 sessions

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If $$y^2 + ky + b = (y − z)(y + q)$$, then what is b, in terms of q and z?

A q + z
B q – z
C qz
D –qz
E q/z

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Joined: 18 Aug 2017
Posts: 1894
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?  [#permalink]

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Updated on: 22 Jan 2019, 03:59
Bunuel wrote:
If $$y^2 + ky + b = (y − z)(y + q)$$, then what is b, in terms of q and z?

A q + z
B q – z
C qz
D –qz
E q/z

I am not sure on how to solve this relation
have marked d as its the closet option i could get..
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Originally posted by Archit3110 on 22 Jan 2019, 03:05.
Last edited by Archit3110 on 22 Jan 2019, 03:59, edited 2 times in total.
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Location: India
Re: If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?  [#permalink]

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22 Jan 2019, 03:10
Bunuel wrote:
If $$y^2 + ky + b = (y − z)(y + q)$$, then what is b, in terms of q and z?

A q + z
B q – z
C qz
D –qz
E q/z

IMO D

If $$y^2 + ky + b = (y − z)(y + q)$$, according to me b here signifies the product of q and z, or else they are the factors of this quadratic equation

example been x^2 + 5x + 6(b) = x(x+2) +3(x+2) = (x+2) (x+3) now since i took b as +ive both the roots were -ive

If we have to get 1 +ive and 1 -ive root

I took an example in which x^2 + x - 6(b) = x(x+3) -2 (x +3) = (x-2) (x+3)
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Joined: 10 Nov 2018
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Re: If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?  [#permalink]

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22 Jan 2019, 03:57
1
Compare the LHS and RHS, for equal powers of variables.

y2+ky+b=y2+y(q-z)+(-qz)

Re: If y^2 + ky + b = (y − z)(y + q), then what is b, in terms of q and z?   [#permalink] 22 Jan 2019, 03:57
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