Multiple choice

If the equation $x^2 - bx + 1 = 0$ does not possess real roots, then

  1. $-3 < b < 3$
  2. $-2 < b < 2$
  3. $b > 2$
  4. $b < -2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For x^2 - bx + 1 = 0 to have no real roots, the discriminant D = b^2 - 4 < 0. So b^2 < 4, which means -2 < b < 2.

AI explanation

A quadratic equation does not possess real roots when its discriminant is strictly less than zero. For the equation $x^2 - bx + 1 = 0$, the discriminant is $(-b)^2 - 4(1)(1) = b^2 - 4$. Setting the discriminant to be less than zero gives $b^2 - 4 < 0$. Solving this inequality gives $b^2 < 4$, which means -2 < b < 2. The correct range is -2 < b < 2.

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