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

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

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 - √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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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 - √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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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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by killer1387 » Fri Apr 13, 2012 2:39 am
IMO D
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by sanju09 » Fri Apr 13, 2012 11:49 pm
killer1387 wrote:IMO D
nice opinion
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