Multiple choice

If the roots of the equation $5{x}^{2}-7x+k=0$ are mutually reciprocal then $k=$

  1. $5$
  2. $2$
  3. $\dfrac {1}{5}$

  4. None of these
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A Correct answer
Explanation

If roots are reciprocal, their product is 1. For ax^2 + bx + c = 0, product of roots is c/a. Here, k/5 = 1, so k = 5.

AI explanation

For the roots of the quadratic equation 5x squared minus 7x plus k equals 0 to be mutually reciprocal, their product must be 1. Using the formula for the product of the roots of ax squared plus bx plus c equals 0, which is c divided by a, we get k divided by 5 equals 1. Solving this gives k equals 5.

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