Factoring the Quadratic Polynomial $a x^2 +b x +c$

Question

I want mathematica to factor the quadratic polynomial $a x^2 +b x +c$ into this standard form $a(x-r_1)(x-r_2)$ with $r_1=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}$ and $r_2=-\frac{b}{2a}-\frac{\sqrt{b^2-4ac}}{2a}$. I tried Factor and its Extension option but I could not get anyting.

Try factorCompletely[a x^2 + b x + c, x] from Daniel's answer to the question @Artes linked. — Michael E2, Mar 07 '18 at 17:29
Closely related Factoring polynomials to factors involving complex coefficients — Artes, Mar 07 '18 at 17:33

David G. Stork · Accepted Answer · 2018-03-07T17:25:46.407

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a Times @@ (y - # & /@ (x /. Solve[a x^2 + b x + c == 0, x]))

edited Mar 07 '18 at 17:25

answered Mar 07 '18 at 17:06

David G. Stork

41,180
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(+1) Thanks. :) But, why they really made Factor? :D Also, you missed the coefficient $a$. :) – Hosein Rahnama Mar 07 '18 at 17:13
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@H.R. This is similar to https://mathematica.stackexchange.com/a/8258/4999 – Michael E2 Mar 07 '18 at 17:28
@MichaelE2: Yes, you are right. I just saw that before you mentioned. :) Thanks by the way. :) – Hosein Rahnama Mar 07 '18 at 17:33

Factoring the Quadratic Polynomial $a x^2 +b x +c$

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