The roots of the given polynomial are α,β. Choose an equation whose roots are their reciprocals.

01 / Standard#Your turn

-2x^2+3x-7=0

Official paper · jm01-2021 · I.5 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use Vieta’s sum and product; the roots are nonzero.

Hint 2

The reciprocal sum is the original sum divided by the original product.

Worked solution

Read the original root relations.
$\alpha+\beta=3/2,\quad\alpha\beta=7/2$
Transform the root relations.
$1/\alpha+1/\beta=3/7,\quad1/(\alpha\beta)=2/7$
Construct the polynomial and clear its denominator.
$x^2-(3/7)x+2/7=0\iff7x^2-3x+2=0$

B: 7x²−3x+2=0.

Checks and common pitfalls: The original roots need not be real for Vieta’s identities to hold.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Read the original root relations.
$\alpha+\beta=3/2,\quad\alpha\beta=7/2$
Transform the root relations.
$1/\alpha+1/\beta=3/7,\quad1/(\alpha\beta)=2/7$
Construct the polynomial and clear its denominator.
$x^2-(3/7)x+2/7=0\iff7x^2-3x+2=0$

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

2021 JM01