Find the parameter range for two distinct real roots.

01 / Standard#Your turn

x^2-6x+k=0

Official paper · jm01-2026 · I.4 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the discriminant.

Hint 2

Distinct real roots require a strict inequality.

Worked solution

E: k<9.

Checks and common pitfalls: At k=9 the two roots coincide.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Compute the discriminant.
$\Delta=(-6)^2-4k=36-4k$
Require positivity and solve.
$36-4k>0\iff k<9$

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

2026 JM01