Question

please answer fast..........
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Answer 1

Answer:

a = 2 and b = 7

Step-by-step explanation:

Let f(x) = x^4 + x^3 + 8x^2 + ax + b

Now,

(x^2 + 1) = 0

x = 1, -1

Now,

By using factor theorem,

(x^2 + 1) is the factor of f(x),

if f(1) = 0 and f(-1) = 0

Then,

f(1) = (1)^4 + (1)^3 + 8(1)^2 + a(1) + b

=> 0 = 1 + 1 + 8 + a + b

=> a + b = -10

Also,

f(-1) = (-1)^4 + (-1)^3 + 8(-1)^2 + a(1) + b

=> 0 = 1 -1 + 8 + a + b

=> a + b = -8

Now,

solve (1) and (2), we get

a = 2 and b = 7

Hope it helps!