Question

Solve: x² + 5x – (a² + a – 6) = 0.

Answer 1

x² + 5x – (a² + a – 6) = 0

⇒ x² + 5x – (a + 3)(a – 2) = 0 

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

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

⇒ x[x + (x + 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.