Question

Find the third degree function that has zeros 7 and −11i, and a value of 663 when x=10.

Answer 1

Answer:

$y = x^3 - 7x^2 + 121x + 847$

Step-by-step explanation:

If -11i is a zero, its conjugate also is a zero, so the zeros are:

7, 11i and -11i.

So we can write the third degree function as:

$y = a(x-7)(x-11i)(x+11i)$

$y = a(x-7)(x^2+121)$

If the function has a value of 663 when x = 10, we have:

$663 = a(10-7)(10^2+121)$

$663 = a(3)(221)$

$a = 663/663 = 1$

So the function is:

$y = (x-7)(x^2+121)$

$y = x^3 - 7x^2 + 121x - 847$