Exercise 51 Page 283

Let's start with highlighting the coefficients of the equation. 3x^2 -5x+ 1=0 Next, we will use the Quadratic Formula to find the roots of the equation. x=- b±sqrt(b^2-4 a c)/2 a In our equation, we can identify the coefficients as a=3, b=-5, and c=1. Now, we will insert the coefficients into the formula and find the roots.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=-( -5)±sqrt(( -5)^2-4( 3)( 1))/2( 3)

CalcPow

Calculate power

x=- (-5)±sqrt(25-4(3)(1))/2(3)

Multiply

Multiply

x=5±sqrt(25-13)/6

SubTerm

Subtract term

x=5±sqrt(13)/6

As a result, we have two roots for the equation. x_1=5+sqrt(13)/6 x_2=5-sqrt(13)/6 Thus, the corresponding option is A.