# The roots of the quadratic equation ax2 bx c = 0 will be reciprocal to each other if

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[ -b - (b^2 -4ac)^1/2 ] [ -b + (b^2 -4ac)^1/2 ] = 4a^2

b^2 - (b^2 -4ac) = 4a^2

b^2 -b^2 +4ac = 4a^2

c = a

ie If a= c then roots of a quadratic equation reciprocal of each other?

eg 3x^2 - 7x + 3 =0

x = [ 7 + 13^1/2 ] / 6 or 6 / [ 7 - 13^1/2 ]

1st root x 2nd root

= 6 / [ 7 + 13^1/2 ] * 6 / [ 7 - 13^1/2 ]

= 36 / (7^2 -13)

= 36 / 36

= 1

so root 1 = 1/ root 2 QED