Q55 - Algebraic inequalities

The correct answer is B) 1 ≤ x ≤ 5.

Step 1 — find the roots. We need two numbers that multiply to 5 and add to −6: −1 and −5.

x² − 6x + 5 = (x − 1)(x − 5), so the roots are x = 1 and x = 5.

Step 2 — think of the parabola. The coefficient of x² is positive, so it opens upwards and is below (or on) the x-axis between the roots. The ≤ sign includes the roots themselves.

Check: x = 3 gives 9 − 18 + 5 = −4 ≤ 0 ✓; x = 0 gives 5 > 0 ✗.

C is the solution of the opposite inequality (≥ 0). A and D use the roots −1 and −5, which come from (x + 1)(x + 5), with the wrong signs.