What is the sum of unique roots of the quadratic equation

Question

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

ankitahyd2013 · Answer

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

Sent from my iPhone using  GMAT Club Forum mobile app

NCRanjan · Answer

+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

NCRanjan · Answer

can someone pls explain the OA

T1101 · Answer

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...

NCRanjan · Answer

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

T1101 · Answer

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?

What is the sum of unique roots of the quadratic equation

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the sum of unique roots of the quadratic equation

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards