Multiple choice

Under which one of the following conditions will the quadratic equation $x^2+mx+2=0$ always have real roots ?

  1. $2\sqrt{3}\le m^2<8$
  2. $\sqrt{3} \le m^2 < 4$
  3. $m^2 \ge 8$
  4. $m^2\le \sqrt{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the quadratic equation x^2 + mx + 2 = 0 to have real roots, the discriminant D = b^2 - 4ac must be >= 0. Here, m^2 - 4(1)(2) >= 0, which simplifies to m^2 - 8 >= 0, or m^2 >= 8.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to always have real roots, its discriminant, given by b^2 - 4ac, must be greater than or equal to zero. Substituting the values from the equation x^2 + mx + 2 = 0, we get m^2 - 4(1)(2) >= 0. This simplifies to m^2 >= 8. Therefore, the equation will have real roots whenever m^2 is greater than or equal to 8.

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