Multiple choice

If the equation $\displaystyle x^{2}-bx+1=0$ 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 < 0. D = (-b)^2 - 4(1)(1) = b^2 - 4. b^2 - 4 < 0 => b^2 < 4 => -2 < b < 2.

AI explanation

For a quadratic equation to have no real roots, its discriminant (D = b^2 - 4ac) must be less than zero. Substituting the coefficients from x^2 - bx + 1 = 0 gives (-b)^2 - 4(1)(1) < 0. Solving b^2 - 4 < 0 results in b^2 < 4, which means -2 < b < 2.

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