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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
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
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25 Apr 2023, 03:06
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
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25 Apr 2023, 05:06
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)
