Find all real zeros, using the given f(1)=0.

01 / Standard#Your turn

f(x)=x^3-3x^2+2

Official paper · jm02-2022 · 2(a)(i) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Divide by x−1.

Hint 2

Solve the remaining quadratic.

Worked solution

x=1, 1−√3, 1+√3.

Checks and common pitfalls: f(1)=0 identifies one root, not all roots.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Factor the cubic.
$f(x)=(x-1)(x^2-2x-2)$
Apply the quadratic formula.
$x=1,\quad x=1\pm\sqrt3$

Think first. Reveal a hint when the class is ready.

2022 JM02