Question

If x2 - 7x + a has a remainder 1 when divided by x + 1, then

Answer 1

Step-by-step explanation:

$let \: f(x) = {x}^{2} - 7x + a \\ and \: remainder \: be \: r(x) \\ consider \: x + 1 = 0 \\ \implies \: x = - 1 \\ \implies \:r( - 1) = 1 \\ now \\ f( - 1) = ({ - 1})^{2} - 7( - 1) + a \\ \therefore \: f( - 1) = 1 + 7 + a \\ \therefore \: f( - 1) = 8 + a \\ \because \: f( - 1) = r( - 1) \\ \therefore \: 8 + a = 1 \\ \therefore \: a = 1 - 8 \\ \huge \fbox{\therefore \: a = - 7}$