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06 Feb 2023, 02:30
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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)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:43) correct
38%
(02:00)
wrong
based on 309
sessions
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What is the equation whose roots are reciprocals of the roots of \(ax^2 + bx + c = 0\)?
A. \(cx^2 + bx + a = 0\)
B. \(cx^2 - bx + a = 0\)
C. \(cx^2 + bx - a = 0\)
D. \(cx^2 - bx - a = 0\)
E. \(cx^2 + bx + a^2 = 0\)
A. \(cx^2 + bx + a = 0\)
B. \(cx^2 - bx + a = 0\)
C. \(cx^2 + bx - a = 0\)
D. \(cx^2 - bx - a = 0\)
E. \(cx^2 + bx + a^2 = 0\)
07 Feb 2023, 05:18
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The quadratic equation whose roots are reciprocal of the roots of the equation \(ax^2 + bx + c = 0 \)
can be obtained by replacing x by \(\frac{1}{x}\).
Thus, the required equation is \(cx^2 + bx + a = 0\).
Answer: A
can be obtained by replacing x by \(\frac{1}{x}\).
Thus, the required equation is \(cx^2 + bx + a = 0\).
Answer: A
General Discussion
Sristishaw
Joined: 27 Jan 2019
Last visit: 21 Sep 2023
Posts: 24
Given Kudos: 52
Location: India
Concentration: Marketing, Human Resources
Schools: HBS '20 Stanford '20 CBS Deferred "24 ISB '27
GMAT 1: 560 Q42 V25
GMAT 2: 610 Q43 V31
GPA: 3.78
WE:Research (Advertising and PR)
12 Feb 2023, 07:16
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Let assume the two roots to be p and q.
Sum of the roots (p+q)=-b/a ........[i]
Product of the roots be (pq)= c/a......[ii]
Now, the reciprocal of the roots will be 1/p and 1/q.
Replace the new roots in the i and ii to find the sum & product of the roots.
And the new equation will be cx^2+bx+a=0.
Answers is A.
Sum of the roots (p+q)=-b/a ........[i]
Product of the roots be (pq)= c/a......[ii]
Now, the reciprocal of the roots will be 1/p and 1/q.
Replace the new roots in the i and ii to find the sum & product of the roots.
And the new equation will be cx^2+bx+a=0.
Answers is A.
