Question

find all the zeros of the polynomial 2x⁴+7x³-19x²-14x+30 it two of its zeros or √2&-√2​

Answer 1

$\huge \fbox \purple{❥ Answer}$

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

Answer 2

Answer:

zeroes of p(x) are √2, -√2, -5, and 3/2