If (1 − p) is a root of quadratic equation x^… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Roots

If $(1 − p)$ is a root of quadratic equation $x^2 + px + (1 − p) = 0$ then its roots are

Answer Choices

Correct answer marked below

0, -1

Correct

-1, 1

0, 1

-1, 2

2, 3

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Explanation

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Official Explanation

Official

Given that:

x^2 + px + (1 − p) = 0

and

x_1 = 1 − p

.

Substitute

x = 1 − p

into the equation:

(1 − p)^2 + p(1 − p) + (1 − p) = 0

Factor out

(1 − p)

(1 − p)[(1 − p) + p + 1] = 0

…

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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.

If (1−p)(1 − p)(1−p) is a root of quadratic equation x2+px+(1−p)=0x^2 + px + (1 − p) = 0x2+px+(1−p)=0 then its roots are