Saved Bookmarks
| 1. |
If two zeros of the polynomial p(x) = 2x4 - 3x? - 3x + 6x - 2 are √2 and√-2, find its other two zeros. |
|
Answer» Step-by-step explanation: Answer Since, it is given that 2
and − 2
are the zeroes of the polynomial p(X)=2x −3x 3 −3x 2 +6x−2, THEREFORE, (x− 2
) and (x+ 2
) are also the zeroes of the given polynomial. Now, consider the PRODUCT of zeroes as follows: (x− 2
)(x+ 2
) =(x) 2 −( 2
) 2 (∵a 2 −b 2 =(a+b)(a−b)) =x 2 −2 We now divide 2x 4 −3x 3 −3x 2 +6x−2 by (x 2 −2) as shown in the above image: From the division, we observe that the quotient is 2x 2 −3x+1 and the remainder is 0. Now, we FACTORIZE the quotient 2x 2 −3x+1 by equating it to 0 to find the other zeroes of the given polynomial: 2x 2 −3x+1=0 ⇒2x 2 −2x−x+1=0 ⇒2x(x−1)−1(x−1)=0 ⇒(2x−1)(x−1)=0 ⇒(2x−1)=0,(x−1)=0 ⇒x= 2 1
,x=1 Hence, the other two zeroes of p(x)=2x 4 −3x 3 −3x 2 +6x−2 are 2 1
,1. |
|