Question

Form a quadratic equation for the given situation:
Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to $k(>0)$ times the wealth he inherited initially. His total assets now stand at a debt of $4$ crore.

• A. $x^2-4x+4=0$
  
• B. $x^2-kx+4=0$
• C. $k{x}^2-kx-4=0$
• D. $x^2-kx-k=0$

Answer 1

The correct option is B $x^2-kx+4=0$

Let the wealth inherited by Vijay be $‘x^{\prime }$ crores. His wealth became $x^2$ because of the soft drinks company. But the toys manufacturing company
brought a loss of $kx$. Now the wealth of Vijay will be $x^2-kx$. This was mentioned to be equal to $-4$ crores.

$\Rightarrow x^2-kx=-4$
$\Rightarrow x^2-kx+4=0$

Hence, the quadratic equation formed is $x^2-kx+4=0$.