Let f be the polynomial function of degree 4 with real coefficients, leading coefficient 1, and roots x = 2 + i, 3, -3. Let g be the polynomial function of degree 4 with intercept (0, -3) and roots x = i, 3i. Find (f + g)(1).

1 Answers

Best Answer

Step 1

The function f(x) is given as:

f(x)=x(x-2-i)(x-3)(x+3)

f(1)=1(1-2-i)(1-3)(1+3)

f(1)=8(1+i)

f(1)=8+8i

g(x)=x(x+3)(x-i)(x-3i)

g(1)=1(1+3)(1-i)(1-3i)

g(1)=4(4-4i)

g(1)=16-16i

Step 2

The required operation is shown as :

(f+g)(1)=8+8i+16-16i

(f+g)(1)=24-8i

The function f(x) is given as:

f(x)=x(x-2-i)(x-3)(x+3)

f(1)=1(1-2-i)(1-3)(1+3)

f(1)=8(1+i)

f(1)=8+8i

g(x)=x(x+3)(x-i)(x-3i)

g(1)=1(1+3)(1-i)(1-3i)

g(1)=4(4-4i)

g(1)=16-16i

Step 2

The required operation is shown as :

(f+g)(1)=8+8i+16-16i

(f+g)(1)=24-8i