Multiple choice

If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then

  1. $b = c$
  2. $a = b$
  3. $ac = 1$
  4. $a = c$
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D Correct answer
Explanation

If roots are alpha and 1/alpha, their product is alpha * (1/alpha) = 1. For a quadratic ax^2 + bx + c = 0, the product of roots is c/a. Thus, c/a = 1, which means a = c.

AI explanation

Let the roots of the quadratic equation be r and 1 divided by r. Using the product of roots formula, which states that the product equals c divided by a, we multiply the roots together. The product of r and 1 divided by r is exactly 1. Setting this equal to c divided by a yields the equation 1 equals c divided by a, which cross-multiplies to a equals c.

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