• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Does y=ax^2+bx+c intersect the x-axis?

This topic has 2 expert replies and 0 member replies

GMAT/MBA Expert

Does y=ax^2+bx+c intersect the x-axis?

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



[Math Revolution GMAT math practice question]

Does y=ax^2+bx+c intersect the x-axis?

1) a<0
2) c>0

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Does y=ax^2+bx+c intersect the x-axis?

1) a<0
2) c>0
\[?\,\,\,\,:\,\,\,\,a{x^2} + bx + c = 0\,\,\,\,{\text{has}}\,\,\left( {{\text{real}}} \right)\,\,{\text{roots?}}\]
\[\left( 1 \right)\,\,\,a < 0\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( { - 1,0,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{Yes}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\,\left[ {y = - {x^2}\,\,\,{\text{parabola}}} \right] \hfill \\
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( { - 1,0, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{No}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\,\left[ {y = - {x^2} - 1\,\,\,{\text{parabola}}} \right] \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,c > 0\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {0,1,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{Yes}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\,\left[ {y = x + 1\,\,{\text{line}}} \right] \hfill \\
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,0,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{No}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\,\left[ {y = {x^2} + 1\,\,\,{\text{parabola}}} \right] \hfill \\
\end{gathered} \right.\]
\[\left( {1 + 2} \right)\,\,\,\,a \ne 0\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,\,:\,\,\,\,\Delta = {b^2} - 4ac\,\,\,\mathop \geqslant \limits^? \,\,\,0\]
\[\left. \begin{gathered}
a < 0\,\, \hfill \\
c > 0 \hfill \\
\end{gathered} \right\}\,\,\,\,\, \Rightarrow \,\,\,\, - 4ac > 0\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{b^2}\,\, \geqslant \,\,0} \,\,\,\,\Delta > 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUF}}.\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
1590 messages
Followed by:
27 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since we are asked about a quadratic polynomial, the question asks if the discriminant b^2-4ac is positive. Neither condition 1) nor condition 2) on its own is sufficient to determine this.

Considering both conditions 1) & 2) together yields b^2-4ac > 0 since b^2 ≥ 0 and ac < 0.

Therefore, C is the answer.
Answer: C

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

199 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 image description Scott@TargetTestPrep

Target Test Prep

109 posts
4 image description Jay@ManhattanReview

Manhattan Review

95 posts
5 image description GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts