Question

find a quadratic polynomial whose one of the zero is minus 50 and sum of the zeros 42

Answer 1

Hey.

Here is the answer.

As sum of zeros is 42.

and one zero is -50

so other zero will be 42 -(-50) = 92

So, the required polynomial will be

(x+50)(x-92)

or, p(x) = x^2 +50 x -92x -4600

or, p(x) = x^2 -42x -4600

Thanks.

Answer 2

Say
$r1 = - 50 \\ r1 + r2 = 42 \\ r2 =42 - r1 \\ r2 = 42 - ( - 50) =92 \\ so \: the \: roots \: are \: r1 = - 50 \: \: \: r2 = 92 \\ so \: the \: polynomial \: can \: be \: written \: as \: \\ (x - 92)(x + 50) = 0 \\ {x}^{2} + 50x - 92x - 4600 = 0 \\ {x}^{2} - 42x - 4600 = 0$