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).

Shyla Odom

Shyla Odom

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2022-08-17

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).

Answer & Explanation

Charlee Beck

Charlee Beck

Beginner2022-08-18Added 6 answers

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

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