Multiple choice

Form the quadratic equation with rational coefficients, if its one of the root is $2\,+\,\sqrt5$, then the equation is

  1. $2x^2\,-\,4x\,-\,1\,=\,0$
  2. $x^2\,-\,2x\,-\,1\,=\,0$
  3. $x^2\,-\,4x\,-\,1\,=\,0$
  4. $x^2\,-\,4x\,-\,2\,=\,0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Turpentine absorbs ozone (O3). A reduction of 20 ml in 100 ml means 20 ml of O3 was present. The reaction 2O3 -> 3O2 shows that 2 volumes of O3 produce 3 volumes of O2, an increase of 1 volume. Since 20 ml of O3 is present, the increase in volume upon heating is 10 ml.

AI explanation

The conjugate root 2 - the square root of 5 is needed for the quadratic equation to have rational coefficients. The sum of the roots is 4, and the product is 2^2 - (the square root of 5)^2 = 4 - 5 = -1. Substituting these values into the formula x^2 - (sum)x + (product) = 0 yields x^2 - 4x - 1 = 0.

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