Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Bunuel after spending 30 minutes pondering where I went wrong just realized that if I chose b=-15 then it becomes the same equation as the second one. In quadratic equations if the constant value changes the root changes. Was taught these things in 8th/9th grade.. This is really embarrassing .. Thanks for replying though atleast my concept got cleared.

I reasoned through this problem a bit different, but it seems like it landed at the right answer. With a root as x-3 and b = 15 for the second equation, you can get to x-5 (can't see another way to get a positive 15) and as a result -8 for a. With two same roots and -8 as a, you know it's (x-some number)^2, and -4 is the only number that fits. (X-4)^2 results in X2 - 8x + 16 and as a result -16 fits.

I'm able to follow along Bunel's solution up to the discriminant point; not sure what a discriminant is!

Substitute a=-8 in the first equation: x^2-8x-b=0.

Now, we know that it has equal roots thus its discriminant must equal to zero: d=(-8)^2+4b=0. Solving for b gives b=-16.

How did you get d=(-8)^2+4b=0.?

The general form of a quadratic equation is \(ax^2+bx+c=0\). It's roots are: \(x_1=\frac{-b-\sqrt{b^2-4ac}}{2a}\) and \(x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}\)

Expression \(b^2-4ac\) is called discriminant:

If discriminant is positive quadratics has two roots;

If discriminant is negative quadratics has no root;

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Please explain how d=(−8)2+4b=0 comes in the question.Kindly explain.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Please explain how d=(−8)2+4b=0 comes in the question.Kindly explain.

Can you explain how you plugged in the values: for the expression b^2−4ac which is called discriminant: I understand if it has same roots, then d must equal 0.

But I do not understand the following because you should be plugging in a = -8 into the equation above, ... i can not follow how you then have -8^2 which should be b^2. And what about variable c? Please help.

\(d=(-8)^2+4b=0\). Solving for \(b\) gives \(b=-16\).
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Can you explain how you plugged in the values: for the expression b^2−4ac which is called discriminant: I understand if it has same roots, then d must equal 0.

But I do not understand the following because you should be plugging in a = -8 into the equation above, ... i can not follow how you then have -8^2 which should be b^2. And what about variable c? Please help.

\(d=(-8)^2+4b=0\). Solving for \(b\) gives \(b=-16\).

Once you get a =-8 and know that as the discriminant for equal roots = 0 ---> from the original equation\(x^2+ax-b=0\),

You can still get this problem if you're like me and aren't totally comfortable with the concept of a discriminant.

Once you get to the point where you figure out a = -8, rephrase the x^2 + ax - b = 0 equation as x^2 - 8x - b = 0 and simply plug in the answer choices, then factor. The equation has "equal roots" so its going to take the form of (x+y)^2 or (x-y)^2.

Starting with C, the equation x^2 - 8x + 15 = 0, but since 15 isn't a perfect square this clearly won't yield equal roots while adding up to -8x.

Moving on to D, the equation becomes x^2 - 8x + 16 = 0; or (x-4)(x-4)=0. It fits.

The other choices don't fit as they don't add up to -8x when factored/foiled.

I think this is a high-quality question and I agree with explanation. Great question! But it appears to be more of a 700 range and not 600.
_________________

You can still get this problem if you're like me and aren't totally comfortable with the concept of a discriminant.

Once you get to the point where you figure out a = -8, rephrase the x^2 + ax - b = 0 equation as x^2 - 8x - b = 0 and simply plug in the answer choices, then factor. The equation has "equal roots" so its going to take the form of (x+y)^2 or (x-y)^2.

Starting with C, the equation x^2 - 8x + 15 = 0, but since 15 isn't a perfect square this clearly won't yield equal roots while adding up to -8x.

Moving on to D, the equation becomes x^2 - 8x + 16 = 0; or (x-4)(x-4)=0. It fits.

The other choices don't fit as they don't add up to -8x when factored/foiled.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I don't understand what is "we know that it has equal roots thus its discriminant must equal to zero: d=(−8)2+4b=0d=(−8)2+4b=0."means.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I don't understand what is "we know that it has equal roots thus its discriminant must equal to zero: d=(−8)2+4b=0d=(−8)2+4b=0."means.

GMAT Club's questions are mostly quite difficulty. One should not attempt them if the fundamentals are not strong enough.