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655-705 (Hard)|   Algebra|   Exponents|      
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MathRevolution
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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 08 Nov 2018, 01:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

68% (02:21) correct 32% (02:41) wrong based on 357 sessions

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Which of the following are roots of an equation \(10x^{-2}+x^{-1}-21=0\)

\(A. \frac{-2}{3}\) or \(\frac{5}{7}\)

\(B. \frac{-2}{3}\) or \(\frac{7}{5}\)

\(C. \frac{2}{3}\) or \(\frac{-5}{7}\)

\(D. \frac{2}{3}\) or \(\frac{-7}{5}\)

\(E. \frac{3}{2}\) or \(\frac{5}{7}\)
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A
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dollytaneja51
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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 08 Nov 2018, 02:36
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Attached is the solution:

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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 08 Nov 2018, 02:29
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MathRevolution
[Math Revolution GMAT math practice question]

Which of the following are roots of an equation \(10x^{-2}+x^{-1}-21=0\)

\(A. \frac{-2}{3}\) or \(\frac{5}{7}\)
\(B. \frac{-2}{3}\) or \(\frac{7}{5}\)
\(C. \frac{2}{3}\) or \(\frac{-5}{7}\)
\(D. \frac{2}{3}\) or \(\frac{-7}{5}\)
\(E. \frac{3}{2}\) or \(\frac{5}{7}\)
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\(\frac{10}{x^2}+\frac{1}{x}-21=0\)
Or, \(10+x-21x^2=0\)
Or, \(-21x^2+x+10=0\) (Standard form of quadratic equation)
Sum of the roots=-(-1/21)=1/21
Product of the roots=-10/21
Only option(A) matches to the above criteria.

Ans. (A)
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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 11 Nov 2018, 23:06
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=>

\(10x^{-2}+x^{-1}-21=0\)
\(=> 10+x-21x^2=0\) by multiplying \(x^2\)
\(=> 21x^2-x-10=0\) by multiplying \((-1)\)
\(=> (3x+2)(7x-5)=0\)
\(=> x =\frac{-2}{3}\) or \(x = \frac{5}{7}\)

Therefore, the answer is A.
Answer: A
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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 05 Sep 2024, 02:10
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A simpler hacky method to solve this using ACs:
For a quadratic equation ax^2+bx+c=0
---> Sum of roots = -b/a
---> Product of roots. = c/a

For the equation 21x^2−x−10=0, sum=(1/21) and product = (-10/21). This eliminates all options other than A
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Which of the following are roots of an equation 10x^{-2}+x^{-1}-21=0 08 Mar 2026, 12:43
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