Question

find the root of this quadratic equation by factorisation method 3root2xsquare-5x-√2=0

Answer 1

3√2x²-5x-√2=0
3√2x²-(6-1)x -√2 = 0
3√2x²- 6x + x-√2=0
3√2x(x-√2)+1(x-√2) = 0
(x-√2)(3√2x+1) = 0
.•. x=√2 or x = -1/3√2
so the roots are √2 & -1/3√2.
Later you can rationalize -1/3√2.
hope u like my answer.

Answer 2

Heya


This is your answer.

Given equation :- 3√2x² - 5x - √2 = 0.

To obtain the roots, we have to factorize it.
Let the do by breaking the middle term.

3√2x² - 5x - √2 = 0
We have to obtain two numbers A and B such that A+B = -5 and AB= √2 X 3√2 = 6.
Looking at the factor of 6, we get 1 and 6.
As, -6 X 1 = AB and A + B = 5.

Clearly, we get -6 and 1.

Breaking the middle term :-
3√2x² -5x- √2 = 0
3√2x² - 6x + x-√2 = 0
3√2x (x-√2) +1(x-√2) = 0
(x - √2)(3√2x + 1) = 0

Comparing with zeroes,  
 (x - √2) = 0  => x = √2
(3√2x + 1) = 0 => x  = -1/3√2.
Hence, the roots are √2 and -1/3√2.
Hope it helps....