Question

if x= -2 is a root of the polynomial -2x4-7x3-tx-10 then find the value of t​

Answer 1

Answer:

$let \: p(x) = - 2 {x}^{4} - 7 {x}^{3} - tx - 10 \: \\ be \: the \: given \: polynomial \\ since \: x = - 2 \: is \: a \: root \: of \: p(x) \\ hence \: \\ p( - 2) = - 2 {( - 2)}^{4} - 7 {( - 2)}^{3} - t( - 2) - 10 \\ = - 32 + 56 + 2t - 10 \\ = 56 - 42 + 2t \\ p( - 2) = 14 + 2t \\ put \: p( - 2) = 0 \\ thereore \\ 14 + 2t = 0 \\ 2t = - 14 \\ t = - \frac{14}{2} \\ t = - 7$