given root 3 is a zero of polynomial x cube + x square - 3 x minus 3 find its other two zeros
IS THIS QUESTION IS RIGHT IF YES THEN HOW COULD I SOLVE THIS
Answers
Step-by-step explanation:
let l,m,nare three roots ,then use formula's:
lm+mn+nl=-b/a=-1
l+m+n=c/a=-3/1=-3
lmn=-d/a=-(-3)/1=3
now u have three equations & three unknown,use these to find l,m,n.
i hope it will help uh!
Answer:
-√3, -1
Step-by-step explanation:
Given polynomial is:
p(x) = x³ + x² - 3x - 3
Since x = √3 is a zero of p(x).
= (x - √3) is a factor of p(x).
Long Division Method:
x - √3) x³ + x² - 3x - 3(x² + (1+√3)x + √3
x³ - √3x²
-------------------------
(1+√3)x² - 3x - 3
(1+√3)x² - (1+√3)√3x
----------------------------------------
(√3 + 3 - 3)x - 3
√3x - 3
-------------------------------------
0
Now,
x² + (1 + √3)x + √3 = 0
⇒ x² + x + √3x + √3 = 0
⇒ x(x + 1) + √3(x + 1) = 0
⇒ (x + √3)(x + 1) = 0
⇒ x = -√3, -1
Hence the two zeroes are: -√3, -1
Hope it helps!