Multiple choice

If the equation x2 - kx + 1=0 does not possess real roots then :

  1. k=-3

  2. -2< k < 2

  3. k>2

  4. k<-2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For no real roots, the discriminant D = b^2 - 4ac < 0. Here, (-k)^2 - 4(1)(1) < 0 => k^2 - 4 < 0 => (k-2)(k+2) < 0. This holds when -2 < k < 2.

AI explanation

For the quadratic equation x^2 - kx + 1 = 0 to have no real roots, its discriminant must be strictly less than zero. The discriminant is D = (-k)^2 - 4(1)(1) = k^2 - 4. Setting the inequality k^2 - 4 < 0 gives k^2 < 4, which means the value of k must be between -2 and 2. Therefore, the condition is -2 < k < 2.

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