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# If a > 0 and b < 0, which of the following statements are t

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If a > 0 and b < 0, which of the following statements are t [#permalink]  15 Jun 2017, 07:37
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Question Stats:

62% (01:31) correct 37% (01:35) wrong based on 24 sessions

If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation $$x^2$$ – ax + b = 0?

Indicate all such statements.

❑ They have opposite signs.

❑ Their sum is greater than zero.

❑ Their product equals –b.

[Reveal] Spoiler: OA
A and B
[Reveal] Spoiler: OA

_________________
Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 330 [0], given: 66

Re: If a > 0 and b < 0, which of the following statements are t [#permalink]  24 Sep 2017, 08:41
My strategy has been to write an example of second degree equation that is easy to solve as x^2-x-4 = 0, where a = 1 and b = -4. This is easily factorized as (x-2)(x+1) = 0 so that the solutions are 2 and -1. Thus, we can screening our choices:

❑ They have opposite signs: 2 and -1 have opposite signs -> CORRECT

❑ Their sum is greater than zero: 2 + (-1) = 1 >0 -> CORRECT

❑ Their product equals –b: 2*(-1) = -2 while b = -4 -> WRONG

Intern
Joined: 01 Jul 2018
Posts: 3
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Kudos [?]: 3 [1] , given: 0

Re: If a > 0 and b < 0, which of the following statements are t [#permalink]  21 Aug 2018, 03:09
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for equation ax^2+bx+c = 0
sum of roots = -b/a
product of roots = c/a

In case of this question:
x^2-ax+b = 0
sum of roots = a (since a> 0 , option b is correct)
product of roots = b (option c incorrect)

product of roots = b and since b is less than 0 , therefore both roots should be of opposite sign (option a correct)
Re: If a > 0 and b < 0, which of the following statements are t   [#permalink] 21 Aug 2018, 03:09
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