Question

Heya!!!
Pls solve the 2nd question.
NEED DETAILED ANSWER.
NO SPAM!!

Answer 1

$\textbf{Your answer is ---}$

Let, f(x) = x^3+5x^2+10k

since, x^3+5x^2+10k leave remainder -2x when divided by x^2+2

Now, subtract -2x from f(x), we get


f(x) = x^3+5x^2+10k+2x


So, f(x) = x^3+5x^2+10k+2x is exactly divide by x^2+2

Now, x^2+2 = 0 => x = √-2

Therefore ,

f(√-2) = 0

=> (√-2)^3+5(√-2)^2+10k-2(√-2) = 0

=> -2(√-2) + 5×-2 + 10k +2(√-2) = 0

=> -10 + 10k = 0

=> k = 10/10

=> $\textbf{ k = 1}$

$\textbf{【 HOPE IT HELPS YOU】 }$