Multiple choice

Bz2 + Cz + D = 0 In the given quadratic equation, B = 9 and C = -12, and D is an integer. What is the least value of D for which the equation has no real roots?

  1. 1

  2. 2

  3. 4

  4. 5
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D Correct answer
Explanation

For no real roots, the discriminant D_q = b^2 - 4ac < 0. Here, (-12)^2 - 4 * 9 * D < 0 => 144 - 36D < 0 => 144 < 36D => D > 4. The least integer D is 5.

AI explanation

Substitute B = 9 and C = -12 into the discriminant formula, which is C squared minus 4 times B times D. This gives 144 minus 36 times D, and for the equation to have no real roots, this value must be strictly less than zero. Solving the inequality 144 minus 36 times D is less than zero yields D is greater than 4. Since D must be an integer, its least possible value is 5.

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