Multiple Choice Question (MCQ)

p^2\geq 4q is the condition for the biquadratic equation x^4+px^2+q=0 to have real roots.

  1. ×

    sufficient but not necessary

  2. necessary but not sufficient

  3. ×

    sufficient and necessary

  4. ×

    neither sufficient nor necessary

Collected in the board: Quartic Equations

Steven Zheng posted 2 weeks ago

Answer

  1. If p^2\geq 4q, the quadratic equation in terms of x^2 has real roots. If the root for x^2 is positive, then x is also real number after taking square root. If the root for x^2 is negative, x will be complex number.

    Therefore, p^2\geq 4q is the necessary but not sufficient condition for the biquadratic equation x^4+px^2+q=0 to have real roots.

Steven Zheng posted 2 weeks ago

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