Multiple choice

The quadratic equation ${ x }^{ 2 }+bx+4=0$ will have real roots if

  1. $b\le -4$ only
  2. $b\ge 4$ only
  3. $-4 < b < 4$
  4. $b\le -4,b\ge 4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For real roots, discriminant D = b^2 - 4ac >= 0. b^2 - 4(1)(4) >= 0. b^2 - 16 >= 0. b^2 >= 16. This means b >= 4 or b <= -4.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to have real roots, the discriminant must be non-negative, meaning b^2 - 4ac >= 0. Here, a = 1, b = b, and c = 4, so the condition is b^2 - 16 >= 0, or b^2 >= 16. This means b <= -4 or b >= 4.

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