Question

Find the roots for the polynomial
y = x(x + 1)(x – 3)(x – 2√2)(x + 2√2).
A. 0, 1, –3
B. 0, –1, 3, –2√2, 2√2
C. –1, 3, –2√2, 2√2
D. 0, 1, –3, –2√2, 2√2

Answer 1

well set each factor to zero and solve

x = 0

x + 1 = 0

x - 3 = 0

etc

solve for x

this will give the roots of the polynomial

Answer 2

so A ?

Answer 3

well you have 2 more to solve...

there are 5 roots...

Answer 4

oh. i guess i dont understand it then

Answer 5

ok... your polynomial is in factored form

so is any of the factors are equal to zero the who polynomial will equal zero.

so to find the zeros you need to left each factor equal zero and solve for the value of x that makes it zero.

so you are solving

x = 0

x + 1 = 0

x - 3 = 0

\[x - 2 \sqrt{2} = 0\]

and

\[x + 2 \sqrt{2} = 0\]

if you solve for x, you are finding where the polynomial cuts the x- axis