Find roots of function

Question

Find roots of the function 

 

f(x)=11^{2x^2-5x+1} -1

 

Express answer in exact form.

Answer 1

Hi Georgina,

 

If 2x² -5x + 1 = 0, then f(x) = 11^{2x^2 -5x + 1} - 1 = 11⁰ - 1 = 1 - 1  = 0

 

Those values of x would be solutions for the function f(x).

 

Then 2x² -5x + 1 = 0

        x = (5 ± √(25 - 4*2*1))/4

           = (5 ± √(17))/4

 

These are roots for f(x)