Quadratics Question

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ntquigley: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Mon Feb 03, 2014 5:24 pm

by ntquigley » Tue Oct 13, 2015 3:29 am

Hello - first time post. My question is an algebraic one on a problem solving question. The question is given an equation for x, what does a quadratic equation for x equal?

Can someone please explain why you cannot just solve for the two roots of the quadratic equation, and since only 1 is in the answer choices, select 1 as the answer?

(x^2+4x+5)=0
factors to:
(x-1)(x+5)=0

negative 5 is not an answer choice, positive 1 IS an answer choice. However, the video describes that the correct answer is 3.

Here is the question and solution. https://www.gmatprepnow.com/module/gmat- ... video/1008

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Source: Beat The GMAT — Problem Solving | Tue Oct 13, 2015 3:29 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Oct 13, 2015 8:09 am

ntquigley wrote:Hello - first time post. My question is an algebraic one on a problem solving question. The question is given an equation for x, what does a quadratic equation for x equal?

Can someone please explain why you cannot just solve for the two roots of the quadratic equation, and since only 1 is in the answer choices, select 1 as the answer?

(x^2+4x+5)=0
factors to:
(x-1)(x+5)=0

negative 5 is not an answer choice, positive 1 IS an answer choice. However, the video describes that the correct answer is 3.

Here is the question and solution. https://www.gmatprepnow.com/module/gmat- ... video/1008

The question is asking you to determine what (x^2+4x+5) equals. Your approach assumes that it equals 0.

Try clearing the fractions with the original question and see what you come up with.

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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 » Tue Oct 13, 2015 8:24 am

Hi ntquigley,

I created this question to expose a common problem that MANY students have when it comes to algebraic expressions.
In most algebra classes, very little time is spent examining expressions on their own, and students all too quickly begin using algebra solely as a way to solve equations. So, in the absence of an equation (e.g., xÂ² + 4x + 5), many students turn the expression into an equation (e.g., xÂ² + 4x + 5 = 0)

However, we don't know that the expression xÂ² + 4x + 5 equals 0. In fact, the goal of the question is to determine what xÂ² + 4x + 5 equals. To do this, we can either determine the value of x (which is a pain) or we can apply some other technique (as is shown in the solution).

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Oct 14, 2015 11:40 pm

Another way of thinking about this: a quadratic equation can be equal to ANYTHING. It doesn't have to be equal to 0, but if we want to solve it, we need to set it equal to 0 through addition/subtraction/whatever. (Well, we don't NEED to, but that's certainly one of the easier ways.)

So if we have, say, xÂ² + 7x + 9 = 3, we'd solve by subtracting 3 from both sides and working out xÂ² + 7x + 6 = 0. But if we were asked for the value of xÂ² + 7x + 9 itself, we'd have to say that it's equal to 3.

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ntquigley: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Mon Feb 03, 2014 5:24 pm

by ntquigley » Thu Oct 15, 2015 7:04 am

Thank you for your detailed responses. I take comfort in the fact knowing that this is a common error.

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