Question

find the value of k, if x-1 is the factor of p(x) =2xsqure +kx+underroot 2​

Answer 1

Step-by-step explanation:

x - 1 is a factor of p(x)

thus x = 1

now

p(x) = 2x² + kx + root 2

$p(x) = 2 {x}^{2} + kx + \sqrt{2} \\ p(1) = 2(1) {}^{2} + k \times 1 + \sqrt{2} \\ p(1) = 2 \times 1 + k + \sqrt{2} \\ p(1) = 2 + k + \sqrt{2 } \\ for \: finding \: \: value \: of \: k \: \\ p(1) = 0 \\ thus \\ \: 2 + k + \sqrt{2} = 0 \\ \\ k = - (2 + \sqrt{2} ) \: ans$