Multiple choice

For the quadratic equation Az2 + Bz + C = 0, A = 13 and B = -10. What is the least integer value of C for which the equation has no real roots?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For no real roots, the discriminant D = B^2 - 4AC < 0. (-10)^2 - 4(13)(C) < 0 => 100 - 52C < 0 => 52C > 100 => C > 100/52 => C > 1.92. The least integer C is 2.

AI explanation

For the quadratic equation Az2 + Bz + C = 0 to have no real roots, its discriminant D = B2 - 4AC must be less than zero. Substituting A = 13 and B = -10 gives (-10)2 - 4(13)C < 0, which simplifies to 100 < 52C. Dividing both sides by 52 results in C > 1.92, making the least integer value of C equal to 2.

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