Multiple choice

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

  1. Real and Distinct Roots

  2. Real and Equal Roots

  3. Imaginary Roots

  4. None of the above
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A Correct answer
Explanation

x + (1+x)^2 = 0 => x + 1 + 2x + x^2 = 0 => x^2 + 3x + 1 = 0. Discriminant D = 3^2 - 4(1)(1) = 9 - 4 = 5. Since D > 0, the roots are real and distinct.

AI explanation

Expand the equation to get x squared plus x plus 1 plus 2x equals 0, which simplifies to x squared plus 3x plus 1 equals 0. The discriminant is b squared minus 4ac, which is 3 squared minus 4 times 1 times 1, equaling 9 minus 4, or 5. Since the discriminant is greater than zero, the equation has real and distinct roots.

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