Question

Other two zeroes of x⁴ – 3x³ + 6x – 4, if two of its zeroes are √2 and -√2

Answer 1

Given:

• A polynomial x⁴-3x³+6x-4 with zeroes √2 and -√2

To Find:

• Other zeroes of given polynomial

Solution:

Let given polynomial be p(x)= x⁴-3x³+6x-4

It is given that √2 and -√2 are the zeroes of given polynomial, then

(x-√2) and (x+√2) will be the factors of p(x)

Also,

(x-√2)(x+√2)= x²-2 will be the the factor of p(x)

Now, on dividing p(x) by x²-2, we will get the other factor

(Calculation in the attachment)

So, x²-3x+2 is the other factor of p(x)

Now,

x²-3x+2

= x²-2x-x+2

= x(x-2)-1(x-2)

= (x-1)(x-2)

So, (x-1) and (x-2) are the factors of p(x)

Therefore, 1 and 2 are the other two zeroes of the p(x)

Answer 2

$\huge\bold\green{\underline{Solution:}}$

Given, √2 , -√2 are zeroes of polynomial

Px=X⁴+3x³+6x-4

therefore,(x-√2)(x+√2)=x²-2

now dividing the given polynomial by x²-2

Find=the other zeroes of polynomial

here refer the attachment ,

•°•X⁴-3X³+6X-4=(X²-2)(X²-3X+2)

(X²-2)(X²-2X-X-2)

(X²-2)(X-2)(X-1)

•°•(x-2)(X-1) are two factor

hence,

x-2=0

X=2

x-1=0

X=1

Therefore, the other 2 zeroes of polynomial are 2,1

$\large{\underline{\red{\rm{AnswEr:2,\:1}}}}$