Question

find all rhe zeros of the polynomial 2x^4+7x³-19x²-14x+30if two of its zeros are √2 amf-√2​

Answer 1

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

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