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.

(i) If six years ago son’s age $=x$ years . The quadratic equation representing the situation is:

[1 mark]

• A. $x^2-x+15=0$
• B. $x^2-2x-15=0$
• C. $2x^2-2x-15=0$
• D. $x^2-2x+15=0$

Answer 1

The correct option is B $x^2-2x-15=0$

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
According to the given statement,
After 9 years,
John’s age = Twice his son’s age
$x^2+15=2\times (x+15)$
$\Rightarrow x^2+15-2x-30=0$
$\Rightarrow x^2-2x-15=0$