Find the sum of the squared roots without solving the quadratic.

01 / Standard#Your turn

2x^2-5x+1=0,\quad\text{roots }\alpha,\beta

Official paper · jm01-2026 · I.6 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the sum and product of roots.

Hint 2

Expand the square of the sum.

Worked solution

Vieta gives both quantities.
$\alpha+\beta=\frac52,\quad\alpha\beta=\frac12$
Subtract twice the product.
$\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta=\frac{25}4-1=\frac{21}4$

C: 21/4.

Checks and common pitfalls: The middle term is 2αβ, not αβ.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Vieta gives both quantities.
$\alpha+\beta=\frac52,\quad\alpha\beta=\frac12$
Subtract twice the product.
$\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta=\frac{25}4-1=\frac{21}4$

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

2026 JM01