If one root of the equation 2x^2 + 3x â€“ k = 0 is 6...

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swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Dec 31, 2017 6:10 am

If one root of the equation 2x^2 + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it of the following way,

If one root is 6, then I can say that 2*6^2 + 3*6 - k=0 and isolate k and get it value, right? . Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Dec 31, 2017 6:10 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 31, 2017 7:21 am

swerve wrote:If one root of the equation 2xÂ² + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10

Your suggested approach is perfect. Here's how it might go...

Since x = 6 is a solution, we know that it SATISFIES the equation 2xÂ² + 3x - k = 0
So, plug x = 6 into the equation to get: 2(6)Â² + 3(6) - k = 0
Simplify: 72 + 18 - k = 0
Solve to get: k = 90

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sun Dec 31, 2017 10:53 am

If one root of the equation 2xÂ² + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10

Hi Swerve,
Let's take a look at your question.

6 is the root of the quadratic equation 2xÂ² + 3x - k = 0, therefore,
$$2\left(6\right)^2+3\left(6\right)-k=0$$
$$2\left(36\right)+3\left(6\right)-k=0$$
$$72+18-k=0$$
$$90-k=0$$
$$k=90$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Aug 18, 2019 6:18 pm

swerve wrote:If one root of the equation 2x^2 + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it of the following way,

If one root is 6, then I can say that 2*6^2 + 3*6 - k=0 and isolate k and get it value, right? . Thanks.

Substituting 6 for x, we have:

2(36) + 3(6) - k = 0

72 + 18 = k

90 = k

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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