Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 weeks ago

How many real roots does the equation x^2 + 3|x| + 2 = 0 have?

6 Answers

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  • 2 weeks ago

    x² + 3|x| + 2 = 0 → you know that a square is always positive or zero.

    x² ≥ 0 → you know that an absolute value is always positive or zero.

    x² + 3|x| ≥ 0 → if you add 2 to the previous value, you can say that:

    x² + 3|x| + 2 > 0 → and you can conclude that

    x² + 3|x| + 2 = 0 ← is no possible

  • Ian H
    Lv 7
    2 weeks ago

    The equation x^2 + 3x + 2 has real roots x = -1 and x = -2 

    But we were not asked about that.  

     

    The graph of y = x^2 + 3|x| + 2 = 0 does not cross the x axis, 

    https://www.wolframalpha.com/input/?i=y+%3D+x%5E2+... 

     so, x^2 + 3|x| + 2 = 0 has no real roots, as is also confirmed by Pope 

    by remarking that for real values the positives on the left can not equal the negative on the right with x^2 + 3|x| = -2 

     

    The equation does have two complex roots. 

  • David
    Lv 7
    2 weeks ago

    If you mean x^2 +3x + 2 = 0 then by solving the quadratic equation x = -1 or x = -2 meaning it has two real roots and when factored it is (x+1)(x+2) = 0

  • sepia
    Lv 7
    2 weeks ago

    x^2 + 3|x| + 2 = 0 

    x^2 + 3x + 2 = 0  or x^2 - 3x + 2 = 0 

    (x + 2)(x + 1) = 0 or (x - 2)(x - 1) = 0

    x^2 + 3|x| + 2 = 0 has 4 real roots.

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  • Pope
    Lv 7
    2 weeks ago

    x² + 3|x| + 2 = 0

    x² + 3|x| = -2

    For all real x, the left side of the equation is non-negative, while the right side is negative. Therefore, no real x satisfies the equation.

  • TomV
    Lv 7
    2 weeks ago

    Assume x < 0

    x² - 3x + 2 = 0

    x² - 2x - x + 2 = 0

    x(x-2) - (x-2) = 0

    (x-1)(x-2) = 0

    x = 1, 2 : invalid solution. Violation of the assumption.

    Assume x > 0

    x² + 3x + 2 = 0

    (x+2)(x+1) = 0

    x = -1, -2 : invalid solution. Violation of the assumption.

    Ans: The equation has no real roots.

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