Multiple choice

Find the value of $k$ for which the equation ${x}^{2}-6x+k=0$ has distinct roots.

  1. $k> 9$
  2. $k=6,7$ only
  3. $k<9$
  4. $k=9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For distinct roots, the discriminant D = b^2 - 4ac > 0. Here, (-6)^2 - 4(1)(k) > 0 => 36 - 4k > 0 => 36 > 4k => k < 9.

AI explanation

A quadratic equation of the form ax^2 + bx + c = 0 has distinct real roots when its discriminant (D = b^2 - 4ac) is strictly greater than zero. Substituting the values from the equation gives (-6)^2 - 4(1)(k) > 0. Simplifying this yields 36 - 4k > 0, or 36 > 4k, which means k < 9.

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