Does x^2 - 9x + 2 < 0 factorize?

If it doesn't, how do I solve it? Thank you

Comments

  • No. It does not factorize.

    To solve an equation of the form x^2 - Bx + C, you have to be able to factorize it as follows:

    (x - M)(x - N)

    where M + N = B, and M(N) = C. There is no solution for this. No pair of whole number factors of 2 add up to anything greater than 3. They would have to add up to 9 for there to be a solution.

    If you are allowed to use numbers that aren't whole numbers, 8.772 and 0.228 will get you REALLY close. They add up to 9 and when you multiply them, you get 2.000016.

  • No, it doesn't factorize.

    Picture the graph of y = x^2 - 9x + 2. It's a parabola that opens upwards.

    It crosses the x-axis twice, at which point y = 0.

    Use the quadratic formula to solve the equation x^2 - 9x + 2 = 0. That gives you the two intercepts.

    x^2 - 9x + 2 < 0 for values of x that are between those intercepts.

  • Use the quadratic equation

  • Use the quadratic formula.

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