Question

If two zeroes of the polynomial x⁴-5x³+3x²+15x-18are √3 and √3 then find the remaining zeroes

Answer 1

too easy yaar
first we have twoo roots √3 and -√3 right
we can write them as (x-√3) and (x+√3)
mulitply both these to get a polynimial 
it is in the form of (a+b) and (a-b) = a²-b² this == x²-3
Now divide the polynomial x⁴-5x³+3x²+15x-18 with x²-3we get quotient as x²-5x+6
on factorising it we get factors 3 and 2
Therefore answer is √3,-√3,3 and 2
Hope my answer is helpful
Please mark it as brainlest

Answer 2

two zeroes are √3 and -√3
So two factors are (x-√3) and (x+√3)

(x-√3)(x+√3) = x² - 3
 x² - 3 is a factor of x⁴-5x³+3x²+15x-18

Now. divide x⁴-5x³+3x²+15x-18 by x²-3
You will get (x² - 5x + 6)

Now find the zeroes of x² - 5x + 6 = 0
⇒ x² - 5x + 6 = 0
⇒ x² - 2x -3x + 6 = 0
⇒ x(x-2) -3(x-2) = 0
⇒ (x-3)(x-2) = 0
⇒ x-3 = 0     and      x-2 = 0
⇒ x = 3    and    x=2

Other two zeroes are 2 and 3.