Question

If alpa and beta are the zeroes of polynomial f(x) =x^2-4x-5 then find the value of alpa^2+beta^2?​

Answer 1

lets find the zeros first

$x^2-4x-5=0\\x^2-5x+x-5=0\\x(x-5)+1(x-5)=0\\(x+1)=0, (x-5)=0\\\\ x=-1 ,5$  

lets suppose $\alpha=-1, \beta=5$

so ${\alpha}^2+{\beta}^2= (-1)^2+(5)^2=1+25=26$