Algebra

posted by .

Solve x(x-7)(x-9)<0 and express the solution set in interval notation.

A. (–infinity, 0)
B. (–infinity, 0) U (7, 9)
C. (–infinity, 0) U (9, infinity)
D. (–infinity, 9)

  • Algebra -

    It is a cubic, with three real zeroes (0,+7 and +9), therefore the graph crosses the x-axis three times.
    The coefficicent of the x³ term is positive, so it increases to the right of the largest root (+9) and decreases to the left of the smallest root (0).
    This tells us that (-∞,0) is a subset of the solution.
    To find the remaining part of the solution, we note that the function is positive between 0 and the next root, and dips below zero again between the last two roots, namely +7 and +9.
    Thus the missing interval is (7,9).
    Can you take it from here?

  • Algebra -

    Based upon your explanation, I am goin to say the answer is

    B(–infinity, 0) U (7, 9)

    ? Is this correct?

  • Algebra -

    Correct!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Inequality

    please check my answers. thanxs! Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. x^2 - 6x + 5 > 0 -I got (-ininity,1) u (5, infinity) x^2 - 3x - 18 < …
  2. Algebra

    Can you please check my answers? Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x-2/x+1 <0 my answer: (-infinity,-1) u (2, infinity) -x+8/x-3 > or
  3. Rational Inequities

    Can you please check my answers? Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x-2/x+1 <0 my answer: (-infinity,-1) u (2, infinity) -x+8/x-3 > or
  4. Algebra

    please check my answers. thanxs! Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. x^2 - 6x + 5 > 0 -I got (-ininity,1) u (5, infinity) x^2 - 3x - 18 < …
  5. Algebra

    f(x)=root sign, and inside that x-2 and g(x)x-7. Which of the following is the domain of the quotient function?
  6. Algebra

    Solve |9 – 4x| > 7 and write interval notation for the solution set. A.(1/2, 4) B. (-4,-1/2) C. (1/2, infinity) D. (-infinity U (4, infinity) I say the answer is D..Am i correct?
  7. Calculus

    Find the horizontal asymptote of f(x)=e^x - x lim x->infinity (e^x)-x= infinity when it's going towards infinity, shouldn't it equal to negative infinity, since 0-infinity = - infinity lim x-> -infinity (e^x)-x= infinity
  8. MATH

    I have been trying to do this problem for a couple of days but i cant seem to get the answer. Any help would be greatly appreciated. For each of the following forms determine whether the following limit type is indeterminate, always …
  9. algebra 2

    what is the domain in interval notation when the restrictions are x cannot = 2 and x cannot = -2?
  10. Math

    Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x?

More Similar Questions