Multiple choice

Solve the following quadratic equation by factorization, the roots are $x^2 \, - \, (\sqrt{3} \, + \, 1)x \, + \, \sqrt{3} \, = \, 0$

  1. $3$, $1$
  2. $\sqrt2$, $1$
  3. $\sqrt3$, $1$
  4. $\sqrt5$, $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation x^2 - (sqrt(3)+1)x + sqrt(3) = 0 can be factored as (x - sqrt(3))(x - 1) = 0. Thus, the roots are sqrt(3) and 1.

AI explanation

To find the roots of x^2 - (sqrt(3) + 1)x + sqrt(3) = 0, we split the middle term to get x^2 - sqrt(3)x - x + sqrt(3) = 0. Factoring by grouping gives x(x - sqrt(3)) - 1(x - sqrt(3)) = 0, which becomes (x - 1)(x - sqrt(3)) = 0. Setting each factor to zero, the roots are 1 and sqrt(3).

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