Question

If ✓2 is a solution of 6x³+✓2x²-10x-4✓2 find it's zeroes

Answer 1

HEY MATE,
HERE UR SOLUTION

Given, √2 is one of the zero of the cubic polynomial.

Then, (x-√2) is one of the factor of the given polynomial p(x) = 6x³+√2x²-10x- 4√2.
Divide p(x) by x-√2

x-√2) 6x³+√2x²-10x-4√2 (6x² +7√2x
   6x³-6√2x²
(-)   (+)
  ----------------------------
7√2x² -10x-4√2
7√2x² -14x
 (-)       (+)
-------------------------
4x   - 4√2
4x   - 4√2
(-)    (+)
---------------------
0

6x³+√2x²-10x-4√2= (x-√2) (6x² +7√2x + 4)

= (x-√2) (6x² +4√2x + 3√2x + 4)

[By splitting middle term]
= (x-√2) [ 2x(3x+2√2) + √2(3x+2√2)
= (x-√2) (2x+√2)   (3x+2√2)

For zeroes of p(x), put p(x)= 0
(x-√2) (2x+√2)  (3x+2√2)= 0
x= √2 , x= -√2/2 ,x= -2√2/3
x= √2 , x= -1 /√2 ,x= -2√2/3
[ Rationalising second zero]

Hence, the other two zeroes of p(x) are -1/√2 and -2√2/3.

HOPE THIS WILL HELP YOU....
THANK-YOU.