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

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Math Revolution GMAT Instructor
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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, 01:36
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[Math Revolution GMAT math practice question]

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

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

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself"  Math Revolution Discount Codes Economist GMAT Tutor Discount Codes Manhattan GMAT Discount Codes Director Status: Learning stage Joined: 01 Oct 2017 Posts: 859 WE: Supply Chain Management (Energy and Utilities) Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0? [#permalink] Show Tags 06 Sep 2018, 01:41 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) _________________ Regards, PKN Rise above the storm, you will find the sunshine Manager Joined: 18 Jul 2018 Posts: 192 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) What is the sum of roots of the equation x^2 – 40x + 399 = 0? [#permalink] Show Tags 06 Sep 2018, 02:18 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 D is the answer. Intern Joined: 02 Sep 2015 Posts: 40 Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0? [#permalink] Show Tags 06 Sep 2018, 03:57 $$x^2-40x+399=0$$ $$x^2-40x+400-1=0$$ $$x^2-40x+400=1$$ $$(x-20)^2=1$$ $$(x-20)=\sqrt{1}$$ $$x-20=1$$ and $$x-20=-1$$ $$x=21$$ and $$x=19$$ Sum of roots=21+19=40 Answer: D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0? [#permalink] Show Tags 09 Sep 2018, 18:26 => 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 $$x$$. Therefore, the answer is D. Answer: D _________________ 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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17 Sep 2018, 18:32
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, 02:33
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, 02:33
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