AlgMap-15.1
Write this quadratic in factored form: [[input:ansf]]\(=0\). [[validation:ansf]] [[feedback:fac]]

Solve this equation, giving your answer as a set \(\left(\mbox{e.g. }\left\{x_1 , x_2\right\}\right)\):

\({@v@} \in \) [[input:ans]] [[validation:ans]][[feedback:prt1]]]]> \({@v@} = {@ta1@}\) or \({@v@} = {@ta2@}\). Therefore our solution set is: \[ {@v@} \in \left\{ {@ta1@} , {@ta2@} \right\}. \]]]> 1 0.1 0 v:rand([x,y,z,t]); cf1:rand(5)+1; cf2:rand(5)+1; a:rand(6)*rand([-1,1]); b:(rand(6)+1)*rand([-1,1]); ta1:-a/cf1; ta2:-b/cf2; \[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@((cf1*v+a)*(cf2*v+b))@} = 0. \] \[ {@v@} \in \left\{ {@ta1@} , {@ta2@} \right\}. \] 1 0 0 *10 none 1 i cos-1 lang [ 0 {"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}} ans algebraic {ta1,ta2} 15 1 0 0 1 1 1 1 1 ansf algebraic (cf1*v+a)*(cf2*v+b) 15 1 0 0 1 1 1 1 1 fac 1.0000000 1 1 0 FacForm ansf (cf1*v+a)*(cf2*v+b) v 0 = 1.0000000 -1 fac-0-T = 0.0000000 -1 fac-0-F prt1 1.0000000 1 1 0 AlgEquiv elementp(?,ans) true 1 = 0.0000000 -1 1-0-T Please replace \(?\) in the answer box with your answer and try again! = 0.0000000 1 1-0-F 1 AlgEquiv ans {ta1, ta2 } 0 = 1.0000000 -1 1-1-T = 0.0000000 -1 1-1-F 2060820372 1584668898 584521279 1003735463 497584038 887938784 1193189753 525135563 198574087 1024221276 1 ans {ta1, ta2} ansf factor((cf1*v+a)*(cf2*v+b)) fac 1.0000000 0.0000000 fac-0-T prt1 1.0000000 0.0000000 1-1-T 2 ans {?,?} ansf ev(expand((cf1*v+a)*(cf2*v+b)),simp) fac 0.0000000 0.1000000 fac-0-F prt1 NULL