Question

Find the value of k.if x-1 is a factor of p(x) .
p(x) = kx²-√2 x+1 ​

Answer 1

${ \bold{ \green{ \underline{ \underline{ANSWER}} : - }}}$

${ \bold{ \underline{Given \: \: function} : - }} \\ \\ { \bold{ \orange{ \: p(x) = k {x}^{2} - \sqrt{2} x + 1}}} \\ \\ { \bold{ \pink{ \mathtt{put \: x = 1 \: in \: equation \: - }}}} \\ \\ { \bold{ \pink{ \mathtt{ \implies \: p(1) = 0}}}} \\ \\ { \bold{ \pink{ \mathtt{ \implies \:p(1) = k - \sqrt{2} + 1 }}}} \\ \\ { \bold{ \pink{ \mathtt{ \implies \:k - \sqrt{2} + 1 = 0}}}} \\ \\ { \bold{ \pink{ \mathtt{ \implies { \boxed{\:k = \sqrt{2} - 1}}}}}}$