In a three dimensional space the equation x2 – 5x + 6 = 0 represents

1.	In a three dimensional space the equation x2 – 5x + 6 = 0 represents A. points B. planes C. curves D. pair of straight lines
Answer» Given: x² – 5x + 6 = 0 x²– 5x + 6 = 0 ⇒ x²– 3x – 2x + 6 = 0 ⇒ x(x – 3) – 2(x – 3) = 0 ⇒ (x – 3)(x – 2) = 0 ⇒ (x – 3) = 0 or (x – 2) = 0 ⇒ x = 3 or x = 2 Both the results represents planes which are parallel to yz-plane Hence, x² – 5x + 6 = 0 represents planes

In a three dimensional space the equation x2 – 5x + 6 = 0 represents A. points B. planes C. curves D. pair of straight lines

Answer»

Given: x² – 5x + 6 = 0

x²– 5x + 6 = 0

⇒ x²– 3x – 2x + 6 = 0

⇒ x(x – 3) – 2(x – 3) = 0

⇒ (x – 3)(x – 2) = 0

⇒ (x – 3) = 0 or (x – 2) = 0

⇒ x = 3 or x = 2

Both the results represents planes which are parallel to yz-plane

Hence, x² – 5x + 6 = 0 represents planes