Question

FIND THE OTHER ZEROES OF THE POLYNOMIAL x4- 5x3+2x2 + 10x-8IF ITS GIVEN THAT TWO OF ITS ZEROES ARE -root2 & root2

Answer 1

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The other zeros are 1 and 4

Answer 2

Answer:

The other zeroes of the polynomial are 1 and 4.

Step-by-step explanation:

The given polynomial is

$p(x)=x^4-5x^3+2x^2+10x-8$

It is given that -√2 and √2 are two zeroes. It means $(x+\sqrt{2})\text{ and }(x-\sqrt{2})$ are factors of p(x).

$(x+\sqrt{2})(x-\sqrt{2})=x^2-2$

Divide the polynomial by $x^2-2$, to find the remaining factors.

Using long division method, we get

$\frac{x^4-5x^3+2x^2+10x-8}{x^2-2}=x^2-5x+4$

Equate the quotient equal to 0, to find the remaining zeroes.

$x^2-5x+4=0$

$x^2-4x-x+4=0$

$x(x-4)-1(x-4)=0$

$(x-4)(x-1)=0$

$x=4,1$

Therefore other zeroes of the polynomial are 1 and 4.