Question

Solve the following quadratic equation:

x² – (2b – 1)x + (b² – b – 20) = 0 

Answer 1

We write, –(2b – 1)x = –(b – 5)x – (b + 4)x as 

x² × (b² – b – 20) = (b² – b – 20)x² = [–(b – 5)x] × [–(b + 4)x] 

∴ x² – (2b – 1)x + (b² – b – 20) = 0 

⇒ x² – (b – 5)x – (b + 4)x + (b + 4) = 0 

⇒ x[x – (b – 5)] – (b + 4)[x – (b – 5)] = 0 

⇒ [x – b – 5][x – (b + 4)] = 0 

⇒ x – (b – 5) = 0 or x – (b + 4) = 0 

⇒ x = b – 5 or x = b + 4 

Hence, b – 5 and b + 4 are the roots of the given equation.