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In how many points does the curve y=x^2-qx+p pass through x-axis?

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In how many points does the curve y=x^2-qx+p pass through x-axis? [#permalink]

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New post 15 Jul 2015, 17:40
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In how many points does the curve \(y=x^2-qx+p\) pass through x-axis?

1) \(q^2>4p\)

2) \(p^2>q\)
[Reveal] Spoiler: OA

Last edited by ENGRTOMBA2018 on 15 Jul 2015, 17:47, edited 1 time in total.
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In how many points does the curve y=x^2-qx+p pass through x-axis? [#permalink]

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New post 16 Jul 2015, 06:55
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The discriminant of the equation is q^{2}- 4p . Discriminant for the equation ax^{2}+bx+c=0 is D=b^{2}-4ac.

Now if
1) b^{2}-4ac > 0, the equation has two roots, i.e it cuts the axis at two points.
2) b^{2}-4ac <0 , no real roots, i.e, it does not cut axis at any point.
3) b^{2}-4ac =0, only one real root, i.e it cuts axis at only 1 point.

Statement 1 : q^{2} > 4p. Even if p is negative, 4p will be less q^{2} and hence D > 0. Two real roots. Two points. Sufficient
Statement 2 : p^{2} > q . Not sufficient.

Hence answer is A
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Re: In how many points does the curve y=x^2-qx+p pass through x-axis? [#permalink]

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New post 21 Nov 2017, 17:29
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Re: In how many points does the curve y=x^2-qx+p pass through x-axis?   [#permalink] 21 Nov 2017, 17:29
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