Lesson: Quadratic Equations

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@0:33 How did you get x^2 + 7x = 0 ?
gmat-admin's picture

All we're saying here is that x^2 + 7x = 0 is a quadratic equation, since we can rewrite this equation in the form ax^2 + bx + c = 0

In the question 9x^2 + 6x + 1=0, I solved it a different way and still got X=-1/3. I multiplied c*a to get 1x9 =9. Then I expanded 6x to get 9x^2+3x+3x+1=0. I then factored the first half to get 3x(3x+1) and 1(3x+1). I was left with x=-1/3
gmat-admin's picture

That's a valid approach too.

If 2ab - c = 2a(b - c), which of the following must be true?

(A) a=0 and c=0
(B) a=1/2 and b=2
(C) b=1 and c=0
(D) a=1 or b=0
(E) a=1/2 or c=0 The answer is E but I fell it could be c also as I started putting figures with c equation and came equal so I choose c .
gmat-admin's picture

Given: 2ab - c = 2a(b - c)
Expand right side: 2ab - c = 2ab - 2ac
Subtract 2ab from both sides: -c = -2ac
Add 2ac to both sides: 2ac - c = 0
Factor: c(2a - 1) = 0

So, EITHER c = 0, OR 2a - 1 = 0
If 2a - 1 = 0, then a = 1/2

So, either c = 0 or a = 1/2 (answer choice E)

The keyword is MUST. Although b = 1 and c = 0 (answer choice C) is a valid solution, it need not be the case that b = 1. Notice that b = 0 and c = 0 also works.

Thanx for the explaination .

How did you get 169?
gmat-admin's picture

You're referring to 6:05 in the video.

We have 3² - (4)(10)(-4) = 9 - (-160)
= 9 + 160
= 169

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