Question

If (y-2)and( y-1/2) are factors of m( y )^2+5y+ n,show that m=n

Answer 1

(y -2) and ( y - 1/2) are the factors of
my² + 5y + n ,

hence, 2 and 1/2 are the zeros of
my² + 5y + n

put, y = 2
m(2)² + 5(2) + n = 0
4m + n = -10 --------(1)

Put y = 1/2
m(1/2)² + 5(1/2) + n = 0
m + 10 + 4n = 0
m + 4n = -10 ------(2)

solve equation (1) and (2)
15n = -30 => n = -2
put n= -2 in equation (1),
4m - 2 = -10
m = -2

hence, m = -2 and n = -2

hence, m = n = -2
proved