Question

What two numbers multiply to -52 and add up to 24

Answer 1

The two numbers are 26 and -2

Explanation:

`let \: we \: take \: the \: two \: numbers \: as \: \alpha \: and \beta \\ by \: the \: given \: data \\ \alpha \beta = - 52 \: and \: \ \: \alpha + \beta = 24 \\ a \: quadratic \: equation \: is \: in \: the \: form \: of \\ {x}^(2) - ( \alpha + \beta )x + \alpha \beta = 0 \\ o n\: substituting \: the \: values \\ {x}^(2) - (24)x - 52 = 0 \\ {x}^(2) - 24x - 52 = 0 \\ by \: factorization \\ (x - 26)(x + 2) = 0 \\ x = 26 \: and \: x = - 2`

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Answer 2

-2 and 26

Explanation:

Multiply to -52:

-2 * 26= -52

Add to 24

-2+26= 24