Multiple choice

Find the nature of the roots for the equation $n^{2}+2\sqrt{2} n+1=0$

  1. Rational & District

  2. Irrational & District

  3. Real & District

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

For n^2 + 2sqrt(2)n + 1 = 0, the discriminant is (2sqrt(2))^2 - 4 = 4, which is positive, so the roots are real and distinct. The roots are -sqrt(2) + 1 and -sqrt(2) - 1, both irrational. Therefore, B is correct.

AI explanation

To find the nature of the roots, evaluate the discriminant using b^2-4ac. For n^2+2(root 2)n+1=0, the discriminant is (2(root 2))^2 - 4(1)(1), which equals 8-4=4. Since the discriminant is positive but not a perfect square, the roots are irrational and distinct.

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