The expression x\(^3\) - 4x\(^2\) + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.
F(X) = x\(^3\) - 4x\(^2\) + cx + d
= (X + 1) Q(X) + R
x = -1, R = 0,f(-1) = -1\(^3\) - 4(-1)\(^2\) + c(-1) + d = 0
-1 - 4 - c + d = 0
d - c = 5................(i)
f(-2) = -2\(^3\) - 4(-2)\(^2\) + c(-2) + d = 1
= -8 - 16 - 2c + d
= 1
-8 - 16 - 2c + d = 1
-24 - 2c + d = 1
d - 2c = 1 + 24
d - 2c = 25.................(ii)
\(\frac{d - c = 5}{-c = 20}\) d - c = 5
c = -20
d - (-20) = 5
d + 20 = 5
d = 5 - 20
= -15
c = -20, d = -15
Contributions ({{ comment_count }})
Please wait...
Modal title
Report
Block User
{{ feedback_modal_data.title }}