Question

John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age.

If six years ago son’s age $=x$ years . The quadratic equation representing the situation will be?
[2 Marks]

Answer 1

Let son’s age six years ago be x years.
∴ John’s age 6 years ago = $x^2$ years
John’s present age $=x^2+6$ years
His son’s present age $=x+6$ years
Hence, after 9 years,
John's age $=x^2+6+9=x^2+15$ years
His son’s age $=x+6+9=x+15$ years
[1 Mark]
According to the given statement,
After 9 years,
John’s age = Twice his son’s age
$x^2+15=2\times (x+15)$
$\Rightarrow x^2+15-2x-30=0$
$\Rightarrow x^2-2x-15=0$
[1 Mark]