Multiple choice

The equation $\left| 1-x \right| +{ x }^{ 2 }=5$ has

  1. A rational root and an irrational root

  2. Two rational

  3. Two irrational roots

  4. No real roots
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Case 1: x >= 1, (x-1) + x^2 = 5 => x^2 + x - 6 = 0 => (x+3)(x-2) = 0. x=2 is a valid root. Case 2: x < 1, (1-x) + x^2 = 5 => x^2 - x - 4 = 0. Using quadratic formula, x = (1 +/- sqrt(1 + 16))/2 = (1 +/- sqrt(17))/2. Since sqrt(17) is irrational, these are irrational roots. Thus, we have one rational root (2) and irrational roots.

Keep practicing — related questions