Multiple choice

Find the equation whose roots are the reciprocals of the roots of $3{x}^{2}-5x+7=0$

  1. $7{x}^{2}-5x+3=0$
  2. $7{x}^{2}+5x+3=0$
  3. $4{x}^{2}-5x+3=0$
  4. $7{x}^{2}-5x+7=0$
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A Correct answer
Explanation

If the roots of ax^2 + bx + c = 0 are r1 and r2, the equation with roots 1/r1 and 1/r2 is cx^2 + bx + a = 0. Swapping the coefficients of x^2 and the constant term gives 7x^2 - 5x + 3 = 0.

AI explanation

To find an equation whose roots are the reciprocals of the roots of 3x^2 - 5x + 7 = 0, substitute x with 1/x in the original equation. This gives 3(1/x)^2 - 5(1/x) + 7 = 0, which simplifies to 3/x^2 - 5/x + 7 = 0. Multiplying the entire equation by x^2 to clear the denominators yields 7x^2 - 5x + 3 = 0.

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