Find all real solutions to the equation (x² − 6x +3)(2x² − 4x − 7) = 0.

x = 3 + √6 ; x = 3 - √6 ; ;  

Step-by-step explanation:

Relation given in the question:

(x² − 6x +3)(2x² − 4x − 7) = 0

Now,

for the above relation to be true the  following condition must be followed:

Either  (x² − 6x +3) = 0 ............(1)

or

(2x² − 4x − 7) = 0 ..........(2)

now considering the equation (1)

(x² − 6x +3) = 0

the roots can be found out as:

for the equation ax² + bx + c = 0

thus,

the roots are

or

or

and, x =

or

and, x =

or

x = 3 + √6 and x = 3 - √6

similarly for (2x² − 4x − 7) = 0.

we have

the roots are

or

or

and, x =

or

and, x =

or

and, x =

or

and,

Hence, the possible roots are

x = 3 + √6 ; x = 3 - √6 ; ;

40 is the final : )