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

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

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New post 06 Sep 2018, 00:36
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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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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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New post 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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New post 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

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

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

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New post 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 \(x\).

Therefore, the answer is D.
Answer: D
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Re: What is the sum of roots of the equation x^2 – 40x + 399 = 0?  [#permalink]

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New post 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.

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

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New post 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:

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

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

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