-3. || , the beroesLa-by a athof the polynomial 23-32212+larefind a an

1.	-3. \|\| , the beroesLa-by a athof the polynomial 23-32212+larefind a and b
Answer» Given polynomial is f(x) = x³ - 3x² + x + 1 . Here a = 1 , b = -3 , c = 1 , d = 1 . Let α = ( a - b ) , β = a and γ = ( a + b ) . As we know, → α + β + γ = -b/a . ⇒ ( a - b ) + a + ( a - b ) = -(-3)/1 . ⇒ 3a = 3 . ⇒ a = 3/3 . ∴ a = 1 . And, → αβ + βγ + γα = c/a . ⇒ a( a - b ) + a( a + b ) + ( a + b )( a - b ) = 1/1 . ⇒ a² - ab + a² + ab + a² - b² = 1 . ⇒ 3a² - b² = 1 . ⇒ ( 3 × 1² ) - b² = 1 . { ∵ a = 1 } ⇒ 3 - b² = 1 . ⇒ b² = 3 - 1 . ⇒ b² = 2 . ∴ b = ±√2 . Hence, it is solved .

-3. || , the beroesLa-by a athof the polynomial 23-32212+larefind a and b

Answer»

Given polynomial is f(x) = x³ - 3x² + x + 1 .

Here a = 1 , b = -3 , c = 1 , d = 1 .

Let α = ( a - b ) , β = a and γ = ( a + b ) .

As we know,

→ α + β + γ = -b/a .

⇒ ( a - b ) + a + ( a - b ) = -(-3)/1 .

⇒ 3a = 3 .

⇒ a = 3/3 .

∴ a = 1 .

And,

→ αβ + βγ + γα = c/a .

⇒ a( a - b ) + a( a + b ) + ( a + b )( a - b ) = 1/1 .

⇒ a² - ab + a² + ab + a² - b² = 1 .

⇒ 3a² - b² = 1 .

⇒ ( 3 × 1² ) - b² = 1 . { ∵ a = 1 }

⇒ 3 - b² = 1 .

⇒ b² = 3 - 1 .

⇒ b² = 2 .

∴ b = ±√2 .

Hence, it is solved .