Question

Find all the zeroes of the polynomial 2x^4+7x^3-19x^2-14x+30 if two of its zeroes are root2 and -root2

Answer 1

other two zeroes of the polynomial are 3/2 and -5

Answer 2

Answer:

Zeroes of polynomial are √2 and -√2

Factor will be  

(x-√2)(x+√2)

=(x²-2)

now, dividing the polynomial with this factor,

x²-2)2x⁴ +7x³ -19x² -14x +30(2x²+7x-15

      2x⁴         -4x²

     -             +

      0     7x³-15x²-14x+30

             7x³        -14x

            -             +

             0    -15x  0   +30

                   -15x       +30

                   +            -  

                    0              0

So, the factors are (x²-2)(2x²+7x-15)

=(x²-2)(2x²+10x -3x -15)

=(x²-2)[2x(x+5)-3(x+5)]

=(x²-2)(x+5)(2x-3)

so, other zeroes are -5 and 3/2