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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # What is the sum of roots of the equation x^2 – 40x + 399 = 0?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the sum of roots of the equation x^2 – 40x + 399 = 0? [#permalink] ### Show Tags 06 Sep 2018, 00:36 00:00 Difficulty: 15% (low) Question Stats: 82% (00:39) correct 18% (01:26) wrong based on 67 sessions ### HideShow timer Statistics [Math Revolution GMAT math practice question] What is the sum of roots of the equation $$x^2 – 40x + 399 = 0$$? $$A. 19$$ $$B. 20$$ $$C. 21$$ $$D. 40$$ $$E. 399$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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06 Sep 2018, 00:41
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the sum of roots of the equation $$x^2 – 40x + 399 = 0$$?

$$A. 19$$
$$B. 20$$
$$C. 21$$
$$D. 40$$
$$E. 399$$

Comparing the given quadratic equation with the standard form of QE, We have
a=1 and b=-40

Sum of roots of QE=-b/a=-(-40)/1=40

Ans. (D)
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What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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06 Sep 2018, 01:18
The general form of the quadratic equation is a$$x^2$$+bx+c = 0.

Sum of the roots is given by $$\frac{-b}{a}$$.

From the given equation a = 1. b = -40. c = 399.

Sum of the roots becomes = $$\frac{-(-40)}{1}$$ = 40

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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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06 Sep 2018, 02:57
1
$$x^2-40x+399=0$$
$$x^2-40x+400-1=0$$
$$x^2-40x+400=1$$
$$(x-20)^2=1$$
$$(x-20)=\sqrt{1}$$
$$x-20=1$$ and $$x-20=-1$$
$$x=21$$ and $$x=19$$
Sum of roots=21+19=40
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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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09 Sep 2018, 17:26
=>

Let $$p$$ and $$q$$ be the roots of the equation $$x^2 – 40x + 399 = 0.$$
Then $$x^2 – 40x + 399 = (x-p)(x-q) = x^2 – (p+q)x + pq.$$
Equating coefficients gives$$p + q = 40$$ from the coefficient of $$x$$.

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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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17 Sep 2018, 17:32
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the sum of roots of the equation $$x^2 – 40x + 399 = 0$$?

$$A. 19$$
$$B. 20$$
$$C. 21$$
$$D. 40$$
$$E. 399$$

In a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots is -b/a. Therefore, here the sum of the roots is -(-40)/1 = 40.

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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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22 Sep 2018, 01:33
While you could find the prime factors $$399$$ and determine that the two roots are $$19$$ and $$21$$, there is a quadratic pattern that we can use to answer this question.

The quadratic equation is given by the general form: $$ax^2$$+$$bx$$+$$c$$$$=0$$, where:

$$a =$$ coefficient of $$x^2$$
$$b =$$ coefficient of $$x$$
$$c =$$ constant

A quadratic equation can have two roots and the sum of its roots is given by $$-b$$ / $$a$$, therefore:

$$sum \ of \ roots = -\frac{b}{a} = - \frac{(-40)}{1} = 40$$

Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0? &nbs [#permalink] 22 Sep 2018, 01:33
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