Answer:
[tex]the \: quadratic \: equation \: is \to \: \\ \boxed{{x}^{2} + \: x \: -20 = 0}.[/tex]
Step-by-step explanation:
[tex]the \: general \: sandard \: form \: is \: given \: by : \\ ax {}^{2} + bx + c = 0 \to \\ since \: the \: roots \: are : \\ 4 \: and \: - 5 \\ we \: apply \: the \: rule \to \\ {x}^{2} - ( \alpha + \beta )x \: + \alpha \beta = 0 \\ therefore \: \to \\ {x}^{2} - ( 4+ ( - 5) )x \: + 4( - 5) = 0 \\ {x}^{2} + \: x \: -20 = 0.[/tex]
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