Question

find all the zeros of the polynomial X raise to power 4 - 3 x cube + 6 x minus 4 if 2 of its zeros are minus root 2 and root 2
pls give the ans briefly

Answer 1

I hope it may help..............plz mark as brainliest..

Answer 2

Answer:

All Zeroes are -√2 , √2 , 2 & 1.

Step-by-step explanation:

we are given with polynomial, $p(x)=x^4-3x^3+6x-4$ and two of its zeroes are -√2 & √2

To find: Other 2 Zeroes

We are given -√2 & √2 as zeroes of p (x).

∴ expression made by zeroes are factors of p (x).

⇒ ( x + √2 ) & ( x - √2 )  are factors of p (x).

⇒ ( x + √2 ) × ( x - √2 ) = x² - 2 is also factor of p (x).

By dividing p (x) with x² - 2  we get another factor of p (x).

Long division is attached in pic.

⇒ p (x) = ( x² - 2 ) ( x² - 3x + 2 )

           = ( x + √2 )  ( x - √2 ) [ x² - 2x - x + 2 ]

           = ( x + √2 )  ( x - √2 ) [ x ( x - 2 ) - ( x - 2 ) ]

           = ( x + √2 )  ( x - √2 ) ( x - 2 ) ( x - 1 )

Zeroes, x - 2 = 0 ⇒ x = 2     and   x - 1 = 0 ⇒ x = 1

Therefore, All Zeroes are -√2 , √2 , 2 & 1.