Question

Weiming solved a quadratic equation with rational coefficients and found that the roots are 2-√3 and 1+√3. Explain why his answer is wrong. ​

Answer 1

According to Viet Theorem the product of the roots must be a rational since all coefficients are rational.

The product of the roots is:

• (2 - √3)(1 + √3) =
• 2 - √3 + 2√3 - (√3)² =
• 2 + √3 - 3 =
• √3 - 1

The product is not rational and therefore the answer is wrong.