Question

Find the zeros of x^4-10x^3+35x^2-50x+24=0

Answer 1

x=1 or x=2 or x=3 or x=4

Explanation:

x4−10x3+35x2−50x+24=0

Step 1: Factor left side of equation.

(x−1)(x−2)(x−3)(x−4)=0

Step 2: Set factors equal to 0.

x−1=0 or x−2=0 or x−3=0 or x−4=0

x=1 or x=2 or x=3 or x=4

Answer 2

Photo is attached.

Sorry my writing is so messy, but basically I found all possible zeros by finding the factors of 24:

(Positive or negative) 1,2,3,4,6,8,12,24

Then, using remainder theorem (when you plug potential zeros into the x values to see if the equation will equal zero) I found out that 1 made the equation equal zero, and therefore was a zero.

Then I used synthetic division to make the equation smaller (I also used 2 because I found out that it was a zero using remainder theorem, same as how I found out 1)


Once I divided it small enough to factor, I simply factored it to find the last 2 zeros

(I didn’t explain everything 100% bc I don’t know how much of this you have learned so if you want clarification on something let me know)