Question

$If the zeroes of the polynomial x3 – 3x2 + x + 1 are a-b, a, a + b, find a and b.$
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Answer 1

Answer:

a = 1

b = ±√2

Step-by-step explanation:

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Answer 2

Since, (a - b), a, (a + b) are the zeroes of the polynomial x³ – 3x² + x + 1.

Therefore, sum of the zeroes = (a - b) + a + (a + b)

= -(-3)/1

= 3

⇒ 3a = 3

⇒ a =1

∴ Sum of the products of is zeroes taken two at a time = a(a - b) + a(a + b) + (a + b) (a - b) =1/1 = 1

a² - ab + a² + ab + a² - b² = 1

⇒ 3a² - b² =1

Putting the value of a,

⇒ 3(1)² - b² = 1

⇒ 3 - b² = 1

⇒ b² = 2

⇒ b = ± √2

Hence, a = 1 and b = ± √2