Question

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Answer 1

Answer:

→ a = 1  and b = ±√2 .

Step-by-step explanation:

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 .

Answer 2

HEYA!

ANSWER-:

Its a cubic polynomial.

And the zeroes are : a-b. , a+b , a

There fore, a-b + a+b + a = -b/a

=> a-b + a+b + a = 3

=> 3a = 3

=> a = 1

Again, (a-b)(a+b)a = -c/a

=> (a-b)(a+b)a = -1

=> (a²-b²)a = -1

=> a³- ab² = -1

=> 1 - b² = -1 ( substituting a= 1)

=> b² = 2

=> b = +_ root over 2

HOPE IT HEPLS YOU