The most common and most likely answer to this crossword clue is the 9 letter word QUADRATIC
I've seen this crossword clue in Financial Times
Q
U
A
D
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Buddy explains!

The straight part
We know that "using roots" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case using roots = quadratic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does QUADRATIC mean?
QUADRATIC noun- A quadratic polynomial, function or equation.
- Square-shaped
- Of a polynomial, involving the second power (square) of a variable but no higher powers, as ax^2 + bx + c.
- Of an equation, of the form ax^2 + bx + c = 0.
- Of a function, of the form y = ax^2 + bx + c .