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.

Expert Answers

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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.


`f=s^2`            (1)

`f+5s=66`  (2)

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.

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