Invertible Polynomials: P2 (R) → P2 (R)

[username123456789]

TL;DR

Stuck in this Invertible polynome

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Let T: P2 (R) → P2 (R) be the linear map defined by T(p(x)) = p''(x) - 5p'(x). Is T invertible ? P2 (R) is the vector space of polynomials of degree 2 or less

 

[Office_Shredder]

For it to be invertible it has to be both 1 to 1 and onto. To start, you might want to just write a polynomial in terms of its coefficients and see what T actually gives.