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

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sanju09 GMAT Instructor
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the quadratic function a x^2 + b x + c = 0 Thu Apr 12, 2012 4:12 am
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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 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
II. The point (5 + √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.

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Shalabh's Quants Really wants to Beat The GMAT!
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Thu Apr 12, 2012 4:48 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 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
II. The point (5 + √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.

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 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0, hence one of the root is (5 - √7). This also implies that (5 + √7)is also a root.

(5 + √7) is the conjugate of (5 - √7). So we know both roots.

...So sum of the roots = 5 + √7 + 5 - √7 = 10.
Product of the roots = (5 - √7). (5 + √7)= 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.

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killer1387 GMAT Destroyer!
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Fri Apr 13, 2012 3:39 am
IMO D

sanju09 GMAT Instructor
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Sat Apr 14, 2012 12:49 am
killer1387 wrote:
IMO D
nice opinion

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The laws of nature are but the mathematical thoughts of God. ~Euclid

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