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What are the two critical points and three possible intervals for this solution?

A.(-8,-6,-4)
B.(-10,-6,0)
C.(-6,0,-6)
D.(-6,0,10)

What are the two critical points and three possible intervals for this solution? A-example-1
User Gregori
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1 Answer

3 votes

Answer:

Explanation:

In this problem the "critical points" are the x-intercepts. Find these by setting x^2 + 12x + 35 = to 0 and solving for x. The coefficients of this quadratic are a = 1, b = 12 and c = 35, and so the discriminant is b^2-4(a)(c) = 144-4(1)(35), or 4.

Thus, the roots (x-intercepts) are:

-12 ± √4 -12 ± 2 -6 ± 1

x = --------------- = --------------- = -------------- = -5 and -7.

The intervals in question are thus (-infinity, -7), (-7, -5), (5, infinity). Possible test points (one from each interval) are { -10, -6, 10}

2(1) 2 1

User Ian Leslie
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