Reading Time: < 1 minute
Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE PS
Solution:
To solve this problem, we need to use the following two facts:
1) If a quadratic equation has integer coefficients only, and if one of the roots is a + √b (where a and b are integers), then a – √b is also a root of the equation.
2) If r and s are roots of a quadratic equation, then the equation is of the form x^2 – (r +s)x + rs = 0.
Since we know that 1 – √2 is a root of the quadratic equation, we can let:
r = 1 + √2
and
s = 1 – √2
Thus, r + s = (1 + √2) + (1 – √2) = 2 and rs = (1 + √2)(1 – √2) = 1 – 2 = -1.
Therefore, the quadratic equation must be x^2 – 2x – 1 = 0.
Answer: D
