Question

obtain all the zeros of 3×4+6×cube-2×square-10×-5, if two of its zeros are √5/3 and -√5/3.

Answer 1

Given: two zeros are √5/3 & - √5/3

so (x-√5/3) & ( x+√5/3) are the factors of the polynomial

(x-√5/3) ( x+√5/3) = x²-5/3 = 3x²-5 is a factor of given polynomial.

Divide the polynomial by this factor.

3x²-5)3x⁴+6x³-2x²-10×-5( x²+2x+1
3x⁴ -5x²
- +
-------------------------
6x³+3x²-10x-5
6x³ -10x
___-_____+_______
3x². -5
3x². -5
___-_____+________

0

x²+2x+1
x²+1x+1x+1
x(x+1) +1(x+1)
(x+1)(x+1)

zeroes are x= -1 & x= -1

Hence all the zeroes are √5/3, √-5/3 ,-1, -1