find a quadratic polynomial whose zeroes are reciprocal of the zeroes of the polynomial ax^2+bx+c
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Let P(x) = 2x2 + 3x - 6.
Given that the polynomial whose zeroes are reciprocal of the zeroes of the polynomial
let x = 1 / x
P(1 / x) = 0
= 2(1 / x)2 + 3(1 / x) - 6 = 0
= 2 + 3x - 6x2 = 0
∴ The reciprocal of the zeroes of the polynomial 6x2 -3x - 2 = 0
Given that the polynomial whose zeroes are reciprocal of the zeroes of the polynomial
let x = 1 / x
P(1 / x) = 0
= 2(1 / x)2 + 3(1 / x) - 6 = 0
= 2 + 3x - 6x2 = 0
∴ The reciprocal of the zeroes of the polynomial 6x2 -3x - 2 = 0
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