Multiple choice

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients. $2s^2-(1+2\sqrt 2)s+\sqrt 2$

  1. $\sqrt 2, \dfrac{3}{2}$
  2. $\sqrt 2,\dfrac{1}{2}$
  3. $\sqrt 2, \dfrac{7}{2}$
  4. $\sqrt 2, \dfrac{9}{2}$
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B Correct answer
Explanation

The polynomial is 2s^2 - (1 + 2*sqrt(2))s + sqrt(2). Factoring gives (2s - 1)(s - sqrt(2)) = 0. The zeroes are s = 1/2 and s = sqrt(2).

AI explanation

To find the zeros of the polynomial 2s^2 - (1 + 2*sqrt(2))s + sqrt(2), set the expression to equal zero and factor it by splitting the middle term. The factors of the product 2*sqrt(2) that add up to -(1 + 2*sqrt(2)) are -1 and -2*sqrt(2). This gives the factored form 2s^2 - 2*sqrt(2)s - s + sqrt(2) = 0, which groups to s(2s - 1) - sqrt(2)(2s - 1) = 0. Factoring out the common term results in (2s - 1)(s - sqrt(2)) = 0. Setting each binomial to zero yields the zeros s = 1/2 and s = sqrt(2).

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