If 8 and 2 are the roots of x2 + ax + c = 0 and 3, 3 are the roots of

1.	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» (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

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»

(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