Question

Find the roots of the following equation, if they exist, by applying the quadratic formula:

4x² + 4bx – (a² – b²) = 0

Answer 1

4x² + 4bx – (a² – b²) = 0 

4x² + 4bx = a² – b² 

(2x)² + 2 × 2x × b + b² = a² – b² + b² = a² – b² + b²   ...(Adding b² on both sides) 

(2x + b)² = a² 

2x + b = ±a   ...(Taking the square root on both sides) 

2x + b = a or 2x + b = –a 

2x = a – b or 2x = –a – b 

`x = (a - b)/2` or `x = -(a + b)/2` 

Hence, `(a - b)/2` and `-(a + b)/2` are the roots of the given equation.