Multiple choice

The least integer $'c'$ which makes the roots of the equation $x^2+3x+2c$ imaginary is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For roots to be imaginary, the discriminant (b^2 - 4ac) must be less than 0. Here, 3^2 - 4(1)(2c) < 0. 9 - 8c < 0. 8c > 9, so c > 1.125. The least integer c is 2.

AI explanation

For the roots of x squared + 3x + 2c equals 0 to be imaginary, the discriminant must be strictly less than zero, giving 3 squared minus 4 times 1 times 2c is less than 0. This simplifies to 9 minus 8c is less than 0, meaning 8c is greater than 9 and c is greater than 9/8. The least integer greater than 9/8 is 2.

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