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Which of the following quadratic equations has at least one root commo
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17 Apr 2023, 01:39

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Which of the following quadratic equations has at least one root common with the quadratic equation \(2x^2 + x – 1 = 0\)

Indicate all that apply

\(x^2 + 5x – 6 = 0\)

\(3x^2 + 5x + 2 = 0\)

\(x^2 + 4x – 5 = 0\)

\(6x^2 + 13x – 8 = 0\)

\(9x^2 + 4x – 5 = 0\)

Indicate all that apply

\(x^2 + 5x – 6 = 0\)

\(3x^2 + 5x + 2 = 0\)

\(x^2 + 4x – 5 = 0\)

\(6x^2 + 13x – 8 = 0\)

\(9x^2 + 4x – 5 = 0\)

Re: Which of the following quadratic equations has at least one root commo
[#permalink]
25 Apr 2023, 03:06

shouldnt it just be c and d

Re: Which of the following quadratic equations has at least one root commo
[#permalink]
25 Apr 2023, 05:06

Expert Reply

OE

We need to check which of the following answer choices has at least one root

common with the equation

2𝑥^2 + 𝑥 − 1 = 0.

First of all, we need to factorize the equation to find its roots.

2𝑥^2 + 𝑥 − 1 = 0

2𝑥^2 + 2𝑥 − 𝑥 − 1 = 0

2𝑥(𝑥 + 1) − 1(𝑥 + 1) = 0

(2𝑥 − 1)(𝑥 + 1) = 0

2𝑥 − 1 = 0 𝑜𝑟 𝑥 + 1 = 0

i.e. 𝑥 = 0.5 𝑜𝑟 𝑥 = −1

A. 𝑥^2 + 5𝑥 − 6 = 0

After factorizing we get, 𝑥

2 + 6𝑥 − 𝑥 − 6 = 0

i.e. 𝑥 = −6 or 𝑥 = 1

Hence, A is not the answer.

B. 3𝑥^2 + 5𝑥 + 2 = 0

After factorizing we get, 3𝑥^2 + 3𝑥 + 2𝑥 + 2 = 0

i.e. 3𝑥 (𝑥 + 1 ) + 2 ( 𝑥 + 1) = 0

i.e. (3𝑥 + 2)(𝑥 + 1) = 0

i.e. 𝑥 = −2/3 or 𝑥 = −1

Hence, B is the answer.

C. 𝑥^2 + 4𝑥 − 5 = 0

After factorizing we get, 𝑥^2 + 5𝑥 − 𝑥 − 5 = 0

i.e. 𝑥 (𝑥 + 5) – 1 (𝑥 + 5) = 0

i.e. (𝑥 − 1) (𝑥 + 5) = 0

i.e. 𝑥 = 1 or 𝑥 = 5

Hence, C is not the answer.

D. 6𝑥^2 + 13𝑥 − 8 = 0

After factorizing we get, 6𝑥^2 + 16𝑥 − 3𝑥 − 8 = 0

i.e. 2𝑥 (3𝑥 + 8) – (3𝑥 + 8) = 0

i.e. (2𝑥 – 1) (3𝑥 + 8 ) = 0

i.e. 𝑥 = 0.5 or 𝑥 = −8/3

Hence, D is the answer.

E. 9𝑥^2 + 4𝑥 − 5 = 0

After factorizing we get, 9𝑥^2 + 9𝑥 − 5𝑥 − 5 = 0

i.e. 9𝑥 (𝑥 + 1) − 5 ( 𝑥 + 1) = 0

i.e. (9𝑥 − 5) (𝑥 + 1) = 0

i.e. 𝑥 = 5/9 or 𝑥 = −1

Hence, the answer is E.

Ans. (B, D, E)

We need to check which of the following answer choices has at least one root

common with the equation

2𝑥^2 + 𝑥 − 1 = 0.

First of all, we need to factorize the equation to find its roots.

2𝑥^2 + 𝑥 − 1 = 0

2𝑥^2 + 2𝑥 − 𝑥 − 1 = 0

2𝑥(𝑥 + 1) − 1(𝑥 + 1) = 0

(2𝑥 − 1)(𝑥 + 1) = 0

2𝑥 − 1 = 0 𝑜𝑟 𝑥 + 1 = 0

i.e. 𝑥 = 0.5 𝑜𝑟 𝑥 = −1

A. 𝑥^2 + 5𝑥 − 6 = 0

After factorizing we get, 𝑥

2 + 6𝑥 − 𝑥 − 6 = 0

i.e. 𝑥 = −6 or 𝑥 = 1

Hence, A is not the answer.

B. 3𝑥^2 + 5𝑥 + 2 = 0

After factorizing we get, 3𝑥^2 + 3𝑥 + 2𝑥 + 2 = 0

i.e. 3𝑥 (𝑥 + 1 ) + 2 ( 𝑥 + 1) = 0

i.e. (3𝑥 + 2)(𝑥 + 1) = 0

i.e. 𝑥 = −2/3 or 𝑥 = −1

Hence, B is the answer.

C. 𝑥^2 + 4𝑥 − 5 = 0

After factorizing we get, 𝑥^2 + 5𝑥 − 𝑥 − 5 = 0

i.e. 𝑥 (𝑥 + 5) – 1 (𝑥 + 5) = 0

i.e. (𝑥 − 1) (𝑥 + 5) = 0

i.e. 𝑥 = 1 or 𝑥 = 5

Hence, C is not the answer.

D. 6𝑥^2 + 13𝑥 − 8 = 0

After factorizing we get, 6𝑥^2 + 16𝑥 − 3𝑥 − 8 = 0

i.e. 2𝑥 (3𝑥 + 8) – (3𝑥 + 8) = 0

i.e. (2𝑥 – 1) (3𝑥 + 8 ) = 0

i.e. 𝑥 = 0.5 or 𝑥 = −8/3

Hence, D is the answer.

E. 9𝑥^2 + 4𝑥 − 5 = 0

After factorizing we get, 9𝑥^2 + 9𝑥 − 5𝑥 − 5 = 0

i.e. 9𝑥 (𝑥 + 1) − 5 ( 𝑥 + 1) = 0

i.e. (9𝑥 − 5) (𝑥 + 1) = 0

i.e. 𝑥 = 5/9 or 𝑥 = −1

Hence, the answer is E.

Ans. (B, D, E)

Re: Which of the following quadratic equations has at least one root commo
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15 Jun 2024, 00:07

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following quadratic equations has at least one root commo [#permalink]

15 Jun 2024, 00:07
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