Find all real zeros of the factorised polynomial.

01 / Standard#Your turn

f(x)=(4x^2-3x+3)(2x^2+6x+3)

Official paper · jm01-2025 · II.2(b) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Set each factor equal to zero.

Hint 2

One factor has negative discriminant.

Worked solution

The first factor has no real zero.
$\Delta_1=9-48=-39<0$
Solve the second factor by the quadratic formula.
$x=\frac{-6\pm\sqrt{36-24}}4=\frac{-3\pm\sqrt3}2$

The real roots are (−3±√3)/2.

Checks and common pitfalls: A degree-four polynomial need not have four real roots.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The first factor has no real zero.
$\Delta_1=9-48=-39<0$
Solve the second factor by the quadratic formula.
$x=\frac{-6\pm\sqrt{36-24}}4=\frac{-3\pm\sqrt3}2$

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

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