the quadratic function a x^2 + b x + c = 0

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Apr 12, 2012 3:12 am

What is the sum of the rational numbers a, b, and c used in the quadratic function in variable x, a x^2 + b x + c = 0?
I. The point (5 - âˆš7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
II. The point (5 + âˆš7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.

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Source: Beat The GMAT — Data Sufficiency | Thu Apr 12, 2012 3:12 am

Shalabh's Quants: Master | Next Rank: 500 Posts; Posts: 134; Joined: Fri Apr 06, 2012 3:11 amFollowed by: 5 members; Thanked: 35 times

by Shalabh's Quants » Thu Apr 12, 2012 3:48 am

sanju09 wrote:What is the sum of the rational numbers a, b, and c used in the quadratic function in variable x, a x^2 + b x + c = 0?
I. The point (5 - âˆš7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
II. The point (5 + âˆš7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.

[spoiler]made up by Sanjeev K Saxena in the services of www.avenuesabroad.com[/spoiler]

One of the form of Quadratic equation is x^2 - Sum of the roots* x + Product of the roots.------(1)

Stat. 1...

As The point (5 - âˆš7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0, hence one of the root is (5 - âˆš7). This also implies that (5 + âˆš7)is also a root.

(5 + âˆš7) is the conjugate of (5 - âˆš7). So we know both roots.

...So sum of the roots = 5 + âˆš7 + 5 - âˆš7 = 10.
Product of the roots = (5 - âˆš7). (5 + âˆš7)= 25 - 7 = 18.

Putting these values in eqn 1.

=> x^2 - 10.x + 18 = 0.

=> or a = 1, b = -10, c =18. => a + b + c = 1 - 10 + 18 = 9.

Stat. 1 is sufficient.

Stat. 2...

By similar logic, we can get a + b + c = 1 - 10 + 18 = 9.

So Stat. 2 is also sufficient.

Shalabh Jain,
e-GMAT Instructor

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killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Fri Apr 13, 2012 2:39 am

IMO D

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Apr 13, 2012 11:49 pm

killer1387 wrote:IMO D

nice opinion

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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