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Question

If α and β are the roots of the equation x2+5x7=0. Then a equation with roots
1α and 1β
is .

A
7x25x1=0
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B
7x2+5x+1=0
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C
7x25x+1=0
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D
7x2+5x1=0
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Solution

The correct option is A 7x25x1=0
The equation, x2+5x7=0 has roots, α and βα+β=5 and α×β=7......(1]
when the roots of a equation are given then its equation is of the form-
x2- (sum of its roots)x + (product of its roots)=0
equation with roots, 1αand 1β is x2 (1α+1β)x+1α×1β=0x2 (α+βα×β)x+1α×β=0
using [1] we get,
7x25x1=0

Alternatively Solution:
If the roots of the new equation are reciprocal of the original equation, then we will replace x with 1x in the original equation.
Hence, a new equation formed will be:
(1x)2+5(1x)7=01+5x7x2x2=01+5x7x2=07x25x1=0

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