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03 Oct 2025, 09:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
69% (00:50) correct
30% (01:20) wrong based on 13 sessions
History
Date
Time
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Which of the following equations has no solutions for x?
A. \(x^2 + 8x = –17\)
B. \(x^2 + 8x = –13\)
C. \(x^2 + 8x = 0\)
D. \(x^2 + 8x = 1\)
E. \(x^2 + 8x = 16\)
A. \(x^2 + 8x = –17\)
B. \(x^2 + 8x = –13\)
C. \(x^2 + 8x = 0\)
D. \(x^2 + 8x = 1\)
E. \(x^2 + 8x = 16\)
04 Oct 2025, 05:40
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Equations whose D<0 are the equations with no solutions for x
Let's check option A
x^2+8x+17 = 0
D = b^2 - 4ac = 8^2 - 4*1*17 = 64-68 = -4
Hence D<0 for this equation
only option A satisfies this condition
Therefore, A
Let's check option A
x^2+8x+17 = 0
D = b^2 - 4ac = 8^2 - 4*1*17 = 64-68 = -4
Hence D<0 for this equation
only option A satisfies this condition
Therefore, A
Updated on: 05 Oct 2025, 02:19
Originally posted by Sajjad1994 on 05 Oct 2025, 02:17.
Last edited by Sajjad1994 on 05 Oct 2025, 02:19, edited 1 time in total.
Last edited by Sajjad1994 on 05 Oct 2025, 02:19, edited 1 time in total.
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Official Explanation
For each answer choice, get zero on one side first. For example, (A) becomes \(x^2 + 8x + 17 =0.\) You can determine the number of real solutions by considering the discriminant, \(b^2 – 4ac\), from the Quadratic Formula. Here, a = 1, b = 8, and c = 17. Then \(b^2 – 4ac = 8^2 – 4 × 1 × 17 = 64– 68 = –4. \) When the discriminant is negative, there are no solutions, since it is not possible to take the square root of a negative number within the real number system. (The discriminant appears under the radical sign in the Quadratic Formula:
Only (A) makes \(b^2 –4ac\) negative.
Answer: A
GMAT-Club-Forum-jcfzm32e.png [ 8.27 KiB | Viewed 299 times ]
For each answer choice, get zero on one side first. For example, (A) becomes \(x^2 + 8x + 17 =0.\) You can determine the number of real solutions by considering the discriminant, \(b^2 – 4ac\), from the Quadratic Formula. Here, a = 1, b = 8, and c = 17. Then \(b^2 – 4ac = 8^2 – 4 × 1 × 17 = 64– 68 = –4. \) When the discriminant is negative, there are no solutions, since it is not possible to take the square root of a negative number within the real number system. (The discriminant appears under the radical sign in the Quadratic Formula:
Only (A) makes \(b^2 –4ac\) negative.
Answer: A
Attachment:
GMAT-Club-Forum-jcfzm32e.png [ 8.27 KiB | Viewed 299 times ]
