Question

If 8 and 2 are the roots of x² + ax + c = 0 and 3, 3 are the roots of x² + ax + b = 0, then the roots of the equation x² + ax + b = 0 are …..

(a) 1, 2 

(b) -1, 1 

(c) 9, 1 

(d) -1, 2

Answer 1

(c) 9, 1

Sum = 8 + 2 = 10 = -a ⇒ a = -10 

Product = 3 × 3 = 9 = b ⇒ b = 9 

Now the equation x² + ax + b = 0 

⇒ x² – 10x + 9 = 0 

⇒ (x - 9) (x – 1) = 0 

x = 1 or 9