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Determine the value(s) for which the rational expression -3z+6/6z^2+14z-80 is undefined.

User John Mee
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1 Answer

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Final answer:

The values for which the rational expression -3z+6/6z^2+14z-80 is undefined are z = 4 and z = -10/3, found by setting the factors of the denominator to zero.

Step-by-step explanation:

To determine the value(s) for which the rational expression -3z+6/6z^2+14z-80 is undefined, we must find the values of z that make the denominator equal to zero. This is equivalent to solving the quadratic equation 6z^2+14z-80 = 0.

First, we factor the quadratic expression:

  • 6z^2+14z-80 can be factored into (2z-8)(3z+10).

Setting each factor equal to zero gives us the values of z that are undefined for the original expression:

  • 2z - 8 = 0 implies z = 4
  • 3z + 10 = 0 implies z = -10/3

Thus, the rational expression is undefined for z = 4 and z = -10/3.

User Rivka
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