Multiple choice

The quadratic equation whose roots are the reciprocals of the roots of my2 + ny + t = 0 is

  1. ny2 + ty + m = 0

  2. ty2 + my + n = 0

  3. ty2 + ny + m = 0

  4. None of the above
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C Correct answer
Explanation

If the roots of my^2 + ny + t = 0 are alpha and beta, the roots of the new equation are 1/alpha and 1/beta. Replacing y with 1/y in the original equation gives m(1/y)^2 + n(1/y) + t = 0. Multiplying by y^2 gives m + ny + ty^2 = 0, or ty^2 + ny + m = 0.

AI explanation

Let the roots of the original equation be r1 and r2. The new equation must have roots 1/r1 and 1/r2. Substitute y = 1/x into the original equation, meaning x = 1/y, to get m(1/y)^2 + n(1/y) + t = 0. Multiplying by y^2 gives t y^2 + n y + m = 0.

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