Question

Trevor is studying a polynomial function f(x). Three given roots of f(x) are –7, 2i, and 7. Trevor concludes that f(x) must be a polynomial with degree 3. Which statement is true?

Answer 1

Answer: B

Explanation:

edge 2023

Answer 2

P(x) = x³-2ix² - 49x + 98i

Explanation:

If the roots of the polynomial P(x) are -7, 2i and 7 then the factors of the polynomial in x is expressed are respectively (x+7), x-2i and x-7

Multiplying the factors together to get the required polynomial function:

P(x) = (x+7)(x-7)(x-2i)

P(x) = (x²-7x+7x-49)(x-2i)

P(x) = (x²-49)(x-2i)

P(x) = x²(x)-x²(2i) - 49x -49(-2i)

P(x) = x³-2ix² - 49x + 98i

Hence the polynomial function with degree 3 is P(x) = x³-2ix² - 49x + 98i