GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 24Get an Extra 30% Off Target Test Prep Plans
08:00 PM EDT
-11:59 PM EDT
Grab 30% off any Target Test Prep GRE plan during our Flash Sale and join Brian and many other students who have used Target Test Prep to score high on the GRE. Just enter the coupon code FLASH30 at checkout to save big.
P and Q are roots
[#permalink]
04 Feb 2018, 15:05
04 Feb 2018, 15:05
Expert Reply
1
Bookmarks
00:00
Question Stats:
83% (00:44) correct
16% (00:42) wrong based on 55 sessions
Hide Show timer Statistics
P and Q are roots of \(x^2 - 9x = 36\)
Quantity A |
Quantity B |
\(P+Q\) |
\(P*Q\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudos for the right solution and explanation
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
Given Kudos: 0
Re: P and Q are roots
[#permalink]
04 Feb 2018, 20:14
04 Feb 2018, 20:14
1
Expert Reply
1
Bookmarks
This is a quadratic equation. The best thing to do with these is shove all terms to one side, setting it equal to zero, and then factor. Usually. In this case we don't need to factor. But let's shove. So
x^2 - 9x = 36
becomes
x^2 - 9x - 36 = 0
This is now in the same format as the classic ax^2 - bx + c equation. Now it's good to know that the roots of an equation will always multiply to make c. And they will always add to make
negative b. Notice the negative! Crucial! Anyway since Quantity A is adding the roots, that should be --9, which is 9. And since Quantity B is multiplying them, we'll get c, which is -36. So A is the answer.
In case you have doubts, let's actually factor this thing to show why the roots multiply to c but add to negative b. Factoring x^2 - 9x - 36 gets us (x - 12)(x + 3). Thus, the roots are 12 and -3. Notice that they multiply to -36, (just like -12 and 3 would multiply to -36), but they add to 9, which is negative b. On the other hand -12 and 3 would add to -9, which is b. Important distinction between the roots and the numbers you see in the factored quadratic.
x^2 - 9x = 36
becomes
x^2 - 9x - 36 = 0
This is now in the same format as the classic ax^2 - bx + c equation. Now it's good to know that the roots of an equation will always multiply to make c. And they will always add to make
negative b. Notice the negative! Crucial! Anyway since Quantity A is adding the roots, that should be --9, which is 9. And since Quantity B is multiplying them, we'll get c, which is -36. So A is the answer.
In case you have doubts, let's actually factor this thing to show why the roots multiply to c but add to negative b. Factoring x^2 - 9x - 36 gets us (x - 12)(x + 3). Thus, the roots are 12 and -3. Notice that they multiply to -36, (just like -12 and 3 would multiply to -36), but they add to 9, which is negative b. On the other hand -12 and 3 would add to -9, which is b. Important distinction between the roots and the numbers you see in the factored quadratic.
Re: P and Q are roots
[#permalink]
05 Feb 2018, 02:42
05 Feb 2018, 02:42
1
Carcass wrote:
P and Q are roots of \(x^2 - 9x = 36\)
Quantity A |
Quantity B |
\(P+Q\) |
\(P*Q\) |
Here let us solve the equation \(x^2 - 9x = 36\)
or it can be written as \(x^2-12x-3x-36=0\)
or (x-12)(x+3)=0
Hence 12 and -3 are the roots of the equation.
Now compare QTY A and QTY B
QTY A = 12 + (-3) = 9
QTY B = 12 * (-3) = -36
Hence QTY A > QTY B. i.e option A
