Question

If - 2 and 3 are the zeroes of the quadratic polynomial x² + (a + 1)x + b, then 

(a) a = -2, b = 6 

(b) a = 2, b = -6 

(c) a = -2, b = -6 

(d) a = 2, b = 6

Answer 1

(c) a = –2, b = –6 

Given: 

–2 and 3 are the zeroes of x² + (a + 1) x + b. 

Now,

 (–2)² + (a + 1) × (–2) + b = 0 

⇒ 4 – 2a – 2 + b = 0 

⇒ b – 2a = –2 ….(1) 

Also, 3² + (a + 1) × 3 + b = 0 

⇒ 9 + 3a + 3 + b = 0 

⇒ b + 3a = –12 ….(2)

On subtracting (1) from (2), 

we get a = –2 

∴ b = –2 – 4 = –6 [From (1)]