1-Find the value of k from which the quadratic equation:(k+4``)X square +(k+1)X+1= 0 has equal root.
2-The age of father is equal to the square of the age of his son.The sum of their age of further are 5 times the age of son is 66 years.Find their ages.
In order to have two identical roots `b^2-4ac` must be equal to 0, where a=k+4, b=k+1 and c=1.
Solve for k using the quadratic formula:
t where a=1, b=-2 and c=-15.
Verification for k=5
Verification for k=-3
Therefore, k=5 and k=-3 are values that make one equal root.
Substitute (1) in (2) and write in the form ax^2+bx+c=0
Factor to solve:
s=6 and s=11
If the son is 6 years old the father is 36 years old. A less likely solution would be the son being 11 years old and the father 121 years old.