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# At how many points does the graph of a quadratic equation cut x axis

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SVP
Joined: 08 Jul 2010
Posts: 1958
Location: India
GMAT: INSIGHT
WE: Education (Education)
At how many points does the graph of a quadratic equation cut x axis [#permalink]

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19 Oct 2017, 04:39
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At how many points does the graph of a quadratic equation cut x axis

1) Sum of the roots is 5
2) Product of the roots is 6

Souce: www.GMATinsight.com
[Reveal] Spoiler: OA

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At how many points does the graph of a quadratic equation cut x axis [#permalink]

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19 Oct 2017, 10:51
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GMATinsight wrote:
At how many points does the graph of a quadratic equation cut x axis

1) Sum of the roots is 5
2) Product of the roots is 6

Souce: http://www.GMATinsight.com

Quadratic equation is of the form $$y=ax^2+bx+c$$. at $$x$$ intercept $$y=0$$

hence $$ax^2+bx+c=0 => x^2+\frac{b}{a}x+\frac{c}{a}=0$$

we need to find the value of $$\frac{b}{a}$$ & $$\frac{c}{a}$$ to arrive at the equation and hence at the $$x$$-intercepts

Statement 1: From Vieta's formula , sum of roots$$=-\frac{b}{a}=5$$, hence $$\frac{b}{a}=-5$$ but nothing mentioned about $$\frac{c}{a}$$. Insufficient

Statement 2: Again from Vieta's formulas, product of roots$$=\frac{c}{a}=6$$. but nothing mentioned about $$\frac{b}{a}$$. Insufficient

Combining 1 & 2 we get all the required values, hence our equation is $$x^2-5x+6=0$$

Find the roots of this equation to know the $$x$$-intercepts

$$x^2-5x+6=(x-3)(x-2)=0$$. therefore $$x$$-intercepts are $$3$$ and $$2$$. Sufficient

Option C
At how many points does the graph of a quadratic equation cut x axis   [#permalink] 19 Oct 2017, 10:51
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