Given that √2 is a zero of the cubic polynomial 6x3 + 2 x2 – 10x – 4√2 , find its other roots
Answers
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....
Bhai mere tera question hi galat hai
√2 . 6x3 + 2 x2 – 10x – 4√2 ka factor hi nahi hai .put kr ke dekh
6(√2)3 + 2(√2)2 - 10√2 - 4√2
12√2 + 4 - 10√2 - 4√2
4-4√2
Chal koi ni
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