Free Practice Question

PS · Problem Solving

655-705

Roots

$x^2+bx-c=0$ ; $b$ and $c$ are positive integers. $u$ and $v$ are roots of the quadratic equation. If $|u|>|v|$ , then which of the following is true?

Answer Choices

Correct answer marked below

u>0

and

v>0

u>0

and

v<0

u<0

and

v>0

Correct

u<0

and

v<0

u=0

and

v<0

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

InaAug 31

Took me a while but the product of roots being negative is the key. Since c is positive and it's -c in the equation, uv = -c < 0, so opposite signs. Then sum of roots = -b < 0, so the negative one has to be bigger in absolute value. Given |u|>|v|, u must be the negative one. So u<0 and v>0.

DevanganaSep 1

Exactly how I did it. The sign of the product is what gives it away immediately.

HarshitaSep 2

Wait, sum of roots is -b? I keep mixing up the signs with the general form. Thanks for writing it out.

ColeApr 22

This one tripped me up at first because I assumed u was the bigger root in value, not absolute value. Once I realized uv = -c, everything clicked.

KaushikMay 5

Same here, the absolute value part is what makes it tricky.

MarcAug 12

Solid 700-level question. The trick is you don't even need to know b and c specifically, just their signs. Nice one.

What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

x2+bx−c=0x^2+bx-c=0x2+bx−c=0; bbb and ccc are positive integers. uuu and vvv are roots of the quadratic equation. If ∣u∣>∣v∣|u|>|v|∣u∣>∣v∣, then which of the following is true?