The stated equation is quadratic and has exactly one real root. Find a.

01 / Standard#Your turn

4a^2x^2+2(a+3)x+9=0

Official paper · jm01-2023 · I.5 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Quadratic means a≠0.

Hint 2

A repeated real root requires discriminant zero.

Worked solution

Set the discriminant equal to zero.
$4(a+3)^2-144a^2=0\iff(a+3)^2=36a^2$
Solve the two linear equations; both satisfy a≠0.
$a+3=\pm6a\implies a=3/5\text{ or }-3/7$

D: a=−3/7 or 3/5.

Checks and common pitfalls: a=0 gives a linear equation and violates the stated quadratic condition.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Set the discriminant equal to zero.
$4(a+3)^2-144a^2=0\iff(a+3)^2=36a^2$
Solve the two linear equations; both satisfy a≠0.
$a+3=\pm6a\implies a=3/5\text{ or }-3/7$

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

2023 JM01