Question

Solve the following quadratic equation:

x² + 5x – (a² + a – 6) = 0

Answer 1

We write, 5x = (a + 3)x – (a – 2)x as  

x² × [–(a² + a – 6)] = –(a² + a – 6)x² = (a + 3)x × [–(a – 2)x] 

∴ x² + 5x – (a² + a – 6) = 0 

⇒ x² + (a + 3)x – (a – 2)x – (a + 3)(a – 2) = 0 

⇒ x[x + (a + 3)] – (a – 2)[x + (a + 3)] = 0 

⇒ [x + (a + 3)][x – (a – 2) = 0] 

⇒ x + (a + 3) = 0 or x – (a – 2) = 0 

⇒ x = –(a + 3) or x = a – 2 

Hence, –(a + 3)  and (a – 2) are the roots of the given equation.