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Which of the following equation has one root in common with 2x2 14x
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12 Apr 2023, 00:20
12 Apr 2023, 00:20
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Which of the following equation has one root in common with \(2x^2 – 14x + 24 = 0\)?
\(x^2 + 1 = 0\)
\(x^2 – 2x – 3 = 0\)
\(x^2 + 6x + 5 = 0\)
\(x^2 – 1 = 0\)
\(x^2 + 5x – 6 = 0\)
\(x^2 + 1 = 0\)
\(x^2 – 2x – 3 = 0\)
\(x^2 + 6x + 5 = 0\)
\(x^2 – 1 = 0\)
\(x^2 + 5x – 6 = 0\)
Re: Which of the following equation has one root in common with 2x2 14x
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26 May 2023, 22:50
26 May 2023, 22:50
Expert Reply
OE
Let us find out roots for 2𝑥^2 − 14𝑥 + 24 = 0
We have, 2𝑥^2 − 14𝑥 + 24 = 0
Divide both sides of the equation by 2, we get 𝑥^2 − 7𝑥 + 12 = 0
𝑥^2 − 4𝑥 − 3𝑥 + 12 = 0
𝑥 (𝑥 − 4) − 3(𝑥 − 4) = 0
(𝑥 – 3)(𝑥 – 4) = 0
𝑥 = 4 or 𝑥 = 3.
So, roots for 2𝑥^2 − 14𝑥 + 24 = 0 are 4 and 3.
Let us check with the answer choices.
𝑥^2 + 1 = 0
𝑥^2 = −1
Here no real root of x exists.
B) 𝑥^2 − 2𝑥 − 3 = 0
𝑥^2 − 3𝑥 + 𝑥 − 3 = 0
We get 𝑥 = 3 and 𝑥 = −1.
Here 3 is the common root with 2𝑥^2 − 14𝑥 + 24 = 0
Since, it is a one answer question and we got that B is satisfying the equation, hence
we do not need to check the remaining answer choices.
Ans. (B)
Let us find out roots for 2𝑥^2 − 14𝑥 + 24 = 0
We have, 2𝑥^2 − 14𝑥 + 24 = 0
Divide both sides of the equation by 2, we get 𝑥^2 − 7𝑥 + 12 = 0
𝑥^2 − 4𝑥 − 3𝑥 + 12 = 0
𝑥 (𝑥 − 4) − 3(𝑥 − 4) = 0
(𝑥 – 3)(𝑥 – 4) = 0
𝑥 = 4 or 𝑥 = 3.
So, roots for 2𝑥^2 − 14𝑥 + 24 = 0 are 4 and 3.
Let us check with the answer choices.
𝑥^2 + 1 = 0
𝑥^2 = −1
Here no real root of x exists.
B) 𝑥^2 − 2𝑥 − 3 = 0
𝑥^2 − 3𝑥 + 𝑥 − 3 = 0
We get 𝑥 = 3 and 𝑥 = −1.
Here 3 is the common root with 2𝑥^2 − 14𝑥 + 24 = 0
Since, it is a one answer question and we got that B is satisfying the equation, hence
we do not need to check the remaining answer choices.
Ans. (B)
gmatclubot
Re: Which of the following equation has one root in common with 2x2 14x [#permalink]
26 May 2023, 22:50
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