Multiple choice

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The roots of x^2 - (sqrt(2)+1)x + sqrt(2) = 0 are found by factoring as (x - sqrt(2))(x - 1) = 0. Thus, the roots are sqrt(2) and 1.

AI explanation

The middle term of x^2 - (sqrt(2) + 1)x + sqrt(2) = 0 can be split to give x^2 - sqrt(2)x - x + sqrt(2) = 0. Factoring by grouping gives x(x - sqrt(2)) - 1(x - sqrt(2)) = 0, which results in (x - 1)(x - sqrt(2)) = 0. The roots of this equation are 1 and sqrt(2). The statement is True.

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