Question

If x = 5 and x = 4 are the roots of the equation ax^2+ bx + 20 = 0, find the values of a and b.​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: given \: quadratic \: equation \: is \: ax^2+ bx + 20 = 0,$

$so \: let \: its \: two \: roots \: be \: \alpha \: and \: \beta \\ here \: \alpha = 5 \\ \beta = 4$

$so \: comparing \: the \: given \: quadratic \: equation \: with \: ax^2+ bx +c = 0, \\ we \: get \: c = 20$

$now \: we \: know \: that \: \alpha \: + \beta=- b \div a \\ \\ so \: then \\ 5 + 4 = - b \div a \\ ie \: \: a = - b \div 9 \: \: \: \: \: (1)$

$so \: also \: we \: know \: that \\ \alpha \beta = c \div a \\ ie \: 5 \times 4 = 20 \div a \\ ie \: 20 = 20 \div a \\ so \: a = 1$

$so \: substitute \: value \: of \: a \: in \: (1) \\ we \: get \: b = - 9$