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
Answers
Answer:
All Zeroes are -√2 , √2 , 2 & 1.
Step-by-step explanation:
we are given with polynomial, 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.