Question

F(z) = (z - 5)(2x + 7) (73 = 3) has zeros at x = -3.5, x=3/7 , x=5 What is the sign of f on the interval 3/7 < x <5?

Answer 1

Answer:     Negative

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Explanation:

3/7 = 0.42857 approximately

Pick a number between that value and 5, not including either endpoint. Let's say we pick x = 2

Plug x = 2 into the f(x) function

f(x) = (x - 5)(2x + 7)(7x-3)

f(2) = (2 - 5)(2*2 + 7)(7*2-3)

f(2) = (2 - 5)(4 + 7)(14-3)

f(2) = (-3)(11)(11)

f(2) = -363

The actual result doesn't matter. All we're after is whether the result is positive or negative. We see the result is negative. This means f(x) is negative when 3/7 < x < 5. The f(x) curve is below the x axis on this interval.