Question

Find all zeroes of the polynomial f(x)=2x^4-3x^3-9x^2+15x-5,if two of its zeroes are √5 and -√5

Answer 1

x = -1

x = (10-√120)/2=5-√ 30 = -0.477

x = (10+√120)/2=5+√ 30 = 10.477

Equation at the end of step  1  :

 (((x3) -  32x2) -  15x) -  5  = 0

Checking for a perfect cube :

x3-9x2-15x-5  is not a perfect cube  

Trying to factor by pulling out :

Factoring:  x3-9x2-15x-5  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -15x-5  

Group 2:  -9x2+x3  

Pull out from each group separately :

Group 1:   (3x+1) • (-5)

Group 2:   (x-9) • (x2)