Question

Please help me answer this

Answer 1

9514 1404 393

Answer:

  a) zeros: -2/3, 6

  b) x < -2/3, signs: -, -; sign of product: +

  -2/3 < x < 6, signs: +, -; sign of product: -

  x > 6, signs: + +; sign of product: +

  c) solution: x < -2/3 ∪ x > 6

Step-by-step explanation:

a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)

  3x +2 = 0   ⇒   x = -2/3

  x -6 = 0   ⇒   x = 6

The zeros of the quadratic are x = -2/3 and x = 6.

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b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.

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c) The solution is where the signs of the factors match:

  x < -2/3 or -6 < x