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Which equation has roots that are the reciprocals of the roots of $3 x^{2} - 7 x + 2 = 0$ ?

Competition practiceAlgebra

A $2 x^{2} - 7 x + 3 = 0$
B $3 x^{2} + 7 x + 2 = 0$
C $2 x^{2} + 7 x + 3 = 0$
D $3 x^{2} - 2 x + 7 = 0$

Step-by-Step Solution

Replace

x

by

1/ x

and multiply by

x^{2} : 3 - 7 x + 2 x^{2} = 0

, i.e.

2 x^{2} - 7 x + 3 = 0

. (Roots 2, 1/3 become 1/2, 3.)

Answer: A)

2 x^{2} - 7 x + 3 = 0

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