There are 2 equations x^2+ax+c and x^2+bx +a : GMAT Problem Solving (PS)
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# There are 2 equations x^2+ax+c and x^2+bx +a

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There are 2 equations x^2+ax+c and x^2+bx +a [#permalink]

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23 Oct 2013, 06:04
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There are 2 equations $$x^2+ax+c$$ and $$x^2+bx +a$$ which have a common root. What is the value of (a+b)?

[Reveal] Spoiler:
Note: I am not too sure of whether the question was value of a+b or max value of a+b but the question was either of these 2.I dont have the answer options as well.This appeared in one of the aptitude papers and I got entangled in this question so wanted to know how to approach this
.
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Re: There are 2 equations x^2+ax+c and x^2+bx +a [#permalink]

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23 Oct 2013, 09:52
There are 2 equations $$x^2+ax+c$$ and $$x^2+bx +a$$ which have a common root. What is the value of (a+b)?

[Reveal] Spoiler:
Note: I am not too sure of whether the question was value of a+b or max value of a+b but the question was either of these 2.I dont have the answer options as well.This appeared in one of the aptitude papers and I got entangled in this question so wanted to know how to approach this
.

The approach to this type of questions depends upon basically two parts.
Sum of roots of the equation and product of the roots of a quadratic equation.

ax^2+bx+c=0 this equation has two roots R and Y.

Sum of roots is given (R+Y) = -b/a

Product of roots is given (R.Y)= c/a

You can write both the equation in this format and try to find a relation between a and b.

+1 Kudos if you like my post.

Thanks,
AB
_________________

Thanks,
AB

+1 Kudos if you like and understand.

Intern
Joined: 07 Jan 2013
Posts: 43
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 22 [0], given: 23

Re: There are 2 equations x^2+ax+c and x^2+bx +a [#permalink]

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24 Oct 2013, 02:52
bhatiamanu05 wrote:
There are 2 equations $$x^2+ax+c$$ and $$x^2+bx +a$$ which have a common root. What is the value of (a+b)?

[Reveal] Spoiler:
Note: I am not too sure of whether the question was value of a+b or max value of a+b but the question was either of these 2.I dont have the answer options as well.This appeared in one of the aptitude papers and I got entangled in this question so wanted to know how to approach this
.

The approach to this type of questions depends upon basically two parts.
Sum of roots of the equation and product of the roots of a quadratic equation.

ax^2+bx+c=0 this equation has two roots R and Y.

Sum of roots is given (R+Y) = -b/a

Product of roots is given (R.Y)= c/a

You can write both the equation in this format and try to find a relation between a and b.

+1 Kudos if you like my post.

Thanks,
AB

I know this formula , so accordingly for the 1st eqn if a1 and a2 are roots and b1 &b2 for 2nd eqn so :

a1+a2=-a, b1+b2=-b
a1a2=c, b1b2=a

now a+b=-(a1+a2+b1+b2)

now if one of the common root is x=a2=b2
a+b=-(a1+x+b1+x)=-(c/x+a/x+2x),,

I am not sure how to proceed after this ,, is there a way we can find out what x is and values of c and a as well?? i remember all the options were numerical values. two of which i remember was -1 and 1
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Re: There are 2 equations x^2+ax+c and x^2+bx +a [#permalink]

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24 Oct 2013, 06:00
There are 2 equations $$x^2+ax+c$$ and $$x^2+bx +a$$ which have a common root. What is the value of (a+b)?

[Reveal] Spoiler:
Note: I am not too sure of whether the question was value of a+b or max value of a+b but the question was either of these 2.I dont have the answer options as well.This appeared in one of the aptitude papers and I got entangled in this question so wanted to know how to approach this
.

Let s,r be the roots of the 1sr equation; t,r be the roots of the 2nd equation (r is the common root of 2 equations; r,s and t do not need to be different).
If a=b then c=a, i.e. a+b = 2c and these equations have 2 common root.
Suppose that $$a\neq b$$, then we have $$r^2 + ar + c =0 = r^2 + br +a$$, which implies $$r = \frac{c-a}{b-a}$$
We also have that:
* s + r = -a
* sr =c
* t + r = -b
* tr =a
YOu can use above relations to solve for t,s and find (a+b) in the form of the answers (the same number can be expressed in may different ways).
Hope that my explanation is useful for you.
Re: There are 2 equations x^2+ax+c and x^2+bx +a   [#permalink] 24 Oct 2013, 06:00
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