Question

Write a quadratic equation in standard form with intergral coefficeints that has the roots 4 and -5.

Answer 1

`the \: quadratic \: equation \: is \to \: \\ \boxed{{x}^(2) + \: x \: -20 = 0}.`

Explanation:

`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.`

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