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What is the sum of unique roots of the quadratic equation

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What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 01 Dec 2018, 10:15
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GMATbuster's Weekly Quant Quiz#11 Ques #4


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What is the sum of unique roots of the quadratic equation \(ax^2+bx+c=0\), where a = 1

(1)b+1 = the least odd prime number.
(2)\(c^2 = 9\)

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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 01 Dec 2018, 10:45
[quote="workout"]

GMATbuster's Weekly Quant Quiz#11 Ques #4


For Questions from earlier quizzes: Click Here


What is the sum of unique roots of the quadratic equation \(ax^2+bx+c=0\), where a = 1

(1)b+1 = the least odd prime number.
(2)\(c^2 = 9\)
IMO-C


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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 01 Dec 2018, 11:21
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+A

Sum of roots = -b/a
a=1

Statmt 1 : b+1= 3, b=2 , a =1 so we get the sum of roots

Stmt2: c2=9 , Doesnt help
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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 02 Dec 2018, 14:38
can someone pls explain the OA
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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 03 Dec 2018, 10:11
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NCRanjan wrote:
can someone pls explain the OA


Feel right into the A trap...

We need to find the roots of the quadratic equation --> Since \(a=1\) we know that \(k*n=c\)and \(k+n=b\)(Where k and n are just integer variables)

S(1) \(b+1=3--> b=2\)

\(b=2=k+n\) but here is the twist, I directly jumped to \(1+1=2\), in this case there is only one unique root...

BUT consider \(3-1=2\), in this case there are two unique roots...

Therefore INSUFFICIENT

S(2) \(C^2=9-->c=+-3\)
Possible cases: \(3*1\) or \(-3*1\) or \(3*-1\) or \(-3*-1\) or even \(\sqrt{3}*\sqrt{3}\)

Not clear if one root or two roots...

Therefore INSUFFICIENT

S(1) + S(2)

This leaves us with only one possible case \(b=2=3-1\) and \(c=3*-1\)

Does it all make sense??? Tried my best...
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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 11 Dec 2018, 09:34
but the question is asking for sum of roots and not the values of roots at all times the sum of roots will always be -b/a

if u know what b is and what a is then sum of roots is discernable

it doest matter if its -1-1 =-2 or -3+1 =-2

doesnt this make sense ? i am sorry for asking again can someone pls explain
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Re: What is the sum of unique roots of the quadratic equation  [#permalink]

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New post 11 Dec 2018, 09:59
NCRanjan wrote:
but the question is asking for sum of roots and not the values of roots at all times the sum of roots will always be -b/a

if u know what b is and what a is then sum of roots is discernable

it doest matter if its -1-1 =-2 or -3+1 =-2

doesnt this make sense ? i am sorry for asking again can someone pls explain


You are correct that we can finde the sum of the roots with \(\frac{-b}{a}\), but this is not what the question is asking...
If you read carefully it asks "What is the sum of unique roots", so only the sum of the unique roots not all roots!

Take a look at my explanation above, there you can see that there can be either one unique root or two unique roots... Therefore 2 different sums!

You would be correct if the question would aks: "What is the sum of roots..."

Does it make sense?
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Re: What is the sum of unique roots of the quadratic equation   [#permalink] 11 Dec 2018, 09:59
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