(Q4)Find all the zeros of 2x
4
-3x
3
-3x
2
+6x-2,If you know that two of its zeros are √2 and -√2
x
2
-
x+
x
2
-2)
x
4
-
x
3
-
x
2
+
x-
x
4
-
x
2
- +
-
x
3
+
2
+
x-
-
x
3
+
x
+ -
2
-
2
-
- +
So,2x
4
-3x
3
-3x
2
+6x-2=(x
2
-2)(
x
2
-
x+
)
Now, by splitting -
x, we factorize 2x
2
-3x+1 as(
x-1)(x-1).So, its zeros are given by x=
1
and x=1. Therefore, the zeros of the given polynomial are √2 and -√2, 1 and
1
Clear