Question

Find all the zeros of the polynomial 4x4-20x3+23x2+5x-6 if two of its zeros are 2 and 3.???

Answer 1

here is u r answer

x =2,3,1/2,-1/2

hope u understand

Answer 2

p(x) = 4x^4 - 20x^3 + 23x^2 + 5x - 6

2 and 3 are zeroes of p(x)

alpha=2

beta=3

alpha+beta= 2+3 = 5

alpha*beta=2*3= 6

x^2-(alpha + beta)x + alpha*beta <------ formula

x^2-5x+6

divide 4x^4 - 20x^3 + 23x^2 + 5x - 6  by x^2-5x+6

x²-5x+6  ) 4x*4-20x³+23x²+5x-6 (  4x²-1

               4x*4-20x³+24x²

                 -----------------------

                                   -x²+5x-6

                                   -x²+5x-6

                               --------------------            

                                          0

splitting the middle term of  4x²-1

  4x² = 1    

x² = 1 /4  

x²  = 1/2 and -1/2

the zeroes other than 2 and 3 are 1/2 and -1/2