If two zeros of the polynomial …
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Sia ? 6 years, 4 months ago
Given polynomial is f(x) = x3 - 3x2 + x + 1
Let {tex} \alpha{/tex} = (a - b), {tex} \beta{/tex} = a and {tex} \gamma{/tex} = (a + b)
Now, {tex} \alpha + \beta + \gamma{/tex} = {tex} - \frac { ( - 3 ) } { 1 }{/tex}
⇒ (a - b) + a + ( a + b ) = 3
⇒ a - b + a + a+ b = 3
⇒ a + a + a = 3
⇒ 3a = 3
⇒ a = 3/3
⇒ a = 1
Also, {tex} \alpha \beta + \beta y + \gamma \alpha = \frac { 1 } { 1 }{/tex}
⇒ (a - b)a + a (a + b) + (a + b)(a - b) = 1
⇒ a2 - ab + a2 +ab + a2 - b2 = 1
⇒ 3a2 - b2 = 1 ( ∵ a = 1)
⇒ 3(1)2 - b2 = 1( ∵ a = 1)
⇒ 3 - b2 = 1
⇒ b2 = 2
⇒ b = {tex} \pm \sqrt{2}{/tex}
Hence, a = 1 and b = {tex} \pm \sqrt{2}{/tex}
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