Multiple choice

State the nature of the given quadratic equation $2x^2 + x+1 = 0$

  1. Real and Distinct

  2. Imaginary

  3. Real and Equal

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2x^2 + x + 1 = 0, the discriminant D = b^2 - 4ac = 1^2 - 4(2)(1) = 1 - 8 = -7. Since D < 0, the roots are imaginary.

AI explanation

To determine the nature of the roots, we calculate the discriminant using the formula b squared minus 4ac. For the quadratic equation 2x squared plus x plus 1 equals zero, the discriminant is 1 squared minus 4 times 2 times 1. This simplifies to 1 minus 8, resulting in negative 7. Because the discriminant is less than zero, the equation has no real roots and the roots are imaginary.

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