Source: Revised GRE PDF 1st Ed. Section 6: Math; #7 (p. 85)

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One of the roots of the equation

One of the roots of the equation (x)x + kx - 6 = 0 is 3, and k is a constant. Quantity A : The value of k Quantity B : -1 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

5 Explanations

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Elizabeth Mendes

I understand how you got each of the factors, but do you know that K is -1 because the terms in the factor added together = -1?

And plugging in 3 directly to the equation is an alternate way to solve?

Aug 10, 2019 • Comment

David Recine, Magoosh Tutor

TO address your first question, we get -1 for K by applying the FOIL method to (x-3)*(x+2). This gets us x^2 + 2x - 3x - 6. 2x - 3x = -1x, so yes, the x terms in the factor combine to make -1.

You're also correct that plugging 3 in for x and solving for k will also get you -1:

(x)x + kx - 6 = 0
(3)3 + 3k - 6 = 0
9 + 3k -6 = 0
3k = 6 - 9
3k = -3
k = -1

Aug 26, 2019 • Reply

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ABHINAV SINGH

I solved by plugging in x=3 in the equation which gives x=-1 hence c

Jun 24, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Abhinav :)

I think you meant to write that when you plugged in x = 3, you found k = -1 :) And so Quantity A = Quantity B, which means the answer is C.

Nice work! :)

Jun 25, 2016 • Reply

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Paula Pingue

My answer was that the relationship can not be determined. I plugged in 3 for x to get - 1 for K, but then I reasoned that the prompt says that ONE of the roots of the equation is 3, but couldn't the root be -3 , -2 , or +2 ? Wouldn't that change the value of K when you plug those in?

Aug 12, 2015 • Comment

Sam Kinsman, Magoosh Tutor

Hi Paula,

A single equation can have more than one root - but that doesn't change the equation itself. You can think of the roots of an equation as the values of x that will make the equation equal 0.

Here we know that k is -1, so the equation is y=x^2-x-6. We know that one of the roots of the equation is 3, and if you plug (x=3) into the equation, then y=0. The other root is (-2), because when (x=-2), y=0. So even though this equation has two different roots, the value of k never changes.

Oct 1, 2015 • Reply

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Denys Gajdamaschko

In these equations, do you just assume that +kx is just the form of the generalized way of writing the equation, so the plus in front of k is not indicative of the actual sign of what k is equal to? ie x^2 - x - 6.

Nov 3, 2013 • Comment

Lucas Fink, Magoosh Tutor

Hi Denys,

Yes, that's right. The operation (addition, subtraction, multiplication, etc.) does not signify whether the value of a variable is positive or negative. So the equation says " + kx", but if either k or x is a negative number, the over value is DECREASED by that term, because we are then adding a negative number, which is the same as subtracting. Does that make sense?

Nov 9, 2013 • Reply

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Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment

I was actually confused by this question because it used the word roots. Isn't 3 a factor of the polynomial not a root?

Aug 27, 2017 • Reply

Jonathan , Magoosh Tutor

Hi,
No -- (x - 3) and (x + 2) are the factors of the polynomial.
The ROOTS of the polynomial are the values of the variable that make the polynomial equal to zero.
x = 3 is a root because is makes the polynomial zero.

Sep 4, 2017 • Reply

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One of the roots of the equation

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Section 6: Math

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