Quadratics Question

Question

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

regor60 · Answer

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.

Brent@GMATPrepNow · Answer

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., x² + 4x + 5), many students turn the expression into an equation (e.g., x² + 4x + 5 = 0)

However, we don't know that the expression x² + 4x + 5 equals 0. In fact, the goal of the question is to determine what x² + 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

Matt@VeritasPrep · Answer

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, x² + 7x + 9 = 3, we'd solve by subtracting 3 from both sides and working out x² + 7x + 6 = 0. But if we were asked for the value of x² + 7x + 9 itself, we'd have to say that it's equal to 3.

ntquigley · Answer

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

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