Question

Find the zeroes of the polynomial 4s2-5s+1 and verify the relationship between zeroes and co-efficients

Answer 1

4s^2-5s+1=0
by splitting middle term
4s^2-4s-s+1=0
4s(s-1)-1(s-1)=0
(4s-1)(s-1)=0
either         or
4s-1=0      s-1=0
4s=1         s=1
s=1/4
here,a=4 b=-5 c=1 α=1/4 β=1
α+β=-c/a                                   αβ=b/a
1/4+1=-(-5/4)                            (1/4)(1)=1/4
5/4=54                                         1/4=1/4
hence verified