{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/746e7112e3834b69a13cbd611ea05ebf\" frameborder=\"0\" width=\"1838\" height=\"1378\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1378,"width":1838,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1378,"thumbnail_width":1838,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/746e7112e3834b69a13cbd611ea05ebf-fb58310cf4070dd4.gif","duration":2642.412,"title":"9FM0 CP2 - Set 4C - Roots of Polynomials V2","description":"I go through several short algebra questions using roots of polynomials and symmetric sums. For the first cubic, I use that singles sum to minus b over a, pairs sum to C over A, and the triple sum to minus D over A, then compute quantities like p plus 2 over q plus 2 over r, and p minus 4 times q minus 4 times r minus 4, and p cubed plus q cubed plus r cubed. I then solve for p and q in another cubic from given root sums and products, and evaluate an expression in a later part. I also factor a quartic using a complex root pair, z equals 3 plus or minus 2i, to get factors z squared minus 6z plus 13, and z squared plus 2z plus 5. There was no action requested from viewers."}