Multiple choice

The equation whose roots are reciprocals of the roots of the $7x^2-19x+5=0$ is

  1. $19x^2-5x+7=0$
  2. $7x^2-19x+5=0$
  3. $5x^2-19x+7=0$
  4. $5x^2-7x+19=0$
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C Correct answer
Explanation

If roots are alpha and beta, the equation with roots 1/alpha and 1/beta is obtained by replacing x with 1/x: 7(1/x)^2 - 19(1/x) + 5 = 0. Multiply by x^2: 7 - 19x + 5x^2 = 0, or 5x^2 - 19x + 7 = 0.

AI explanation

To find the equation whose roots are reciprocals of the roots of 7x^2 - 19x + 5 = 0, substitute x with 1/x. This gives 7(1/x)^2 - 19(1/x) + 5 = 0, which simplifies to 7 - 19x + 5x^2 = 0 when multiplied by x^2. Rearranging the terms yields 5x^2 - 19x + 7 = 0.

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