Question -
Answer -
Given, √2 is one ofthe zero of the cubic polynomial.
Then, (x-√2) is one ofthe factor of the given polynomial p(x) = 6x³+√2x²-10x- 4√2.
So, by dividing p(x)by x-√2
6x³+√2x²-10x-4√2=(x-√2) (6x² +7√2x + 4)
By splitting themiddle term,
We get,
(x-√2) (6x² + 4√2x +3√2x + 4)
= (x-√2) [ 2x(3x+2√2)+ √2(3x+2√2)]
= (x-√2) (2x+√2) (3x+2√2)
To get the zeroes ofp(x),
Substitute p(x)= 0
(x-√2) (2x+√2) (3x+2√2)= 0
x= √2 , x= -√2/2 ,x=-2√2/3
Hence, the other twozeroes of p(x) are -√2/2 and -2√2/3