Question

Which is the polynomial equation of lowest degree that has –10, –1, 3, and 4 as roots? f(x) = (x – 10)(x – 1)(x + 3)(x + 4) f(x) = x(x – 10)(x – 1)(x + 3)(x + 4) f(x) = (x + 10)(x + 1)(x – 3)(x – 4) f(x) = x(x + 10)(x + 1)(x – 3)(x – 4)

Answer 1

Answer:

f(x) = (x + 10)(x + 1)(x – 3)(x – 4)

Step-by-step explanation:

If the roots are -10. -1, 3, and 4 then look for factors (x+10)(x+1)(x-3)(x-4) since factors have the opposite sign of the root. This means

f(x) = (x – 10)(x – 1)(x + 3)(x + 4)

f(x) = x(x – 10)(x – 1)(x + 3)(x + 4)

are NOT solutions.

Lowest degree means no extra variables are added. This means

f(x) = x(x + 10)(x + 1)(x – 3)(x – 4)

is NOT a solution,

The solution is f(x) = (x + 10)(x + 1)(x – 3)(x – 4).