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If the zeroes of the polynomial x^3- 3x^2 + x + 1 are a- b,

Question

If the zeroes of the polynomial $x^{3} - 3 x^{2} + x + 1$ are $a - b, a, a + b$ find $a$ and $b$ .

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Oliver Discussed

If the zeroes of the polynomial

x^{3} - 3 x^{2} + x + 1

are

a - b, a, a + b

find

a

and

b

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

P (x) =

x^{3} - 3 x^{2} + x + 1

zeroes are

a - b, a, a + b

Comparing the given polynomial with

p x^{3} + q x^{2} + r x + t

, we obtain

p = 1, q = - 3, r = 1, t = 1

Sum of zeroes =

a - b + a + a + b = \frac{- q}{p} = 3 a

⟹ \frac{- q}{p} = 3 a

⟹ \frac{- ( - 3 )}{1} = 3 a

⟹ 3 = 3 a

⟹ a = 1

\Rightarrow

Then the zeroes becomes,

1 - b, 1, 1 + b

\Rightarrow

Multiplication of zeroes

= (1 - b) \times 1 \times (1 + b) = \frac{- t}{p} = 1 - b^{2}

⟹ \frac{- 1}{1} = 1 - b^{2}

⟹ b^{2} = 2

b = \pm 2

Therefore,

a = 1

and

b =

\pm 2

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Question Text	If the zeroes of the polynomial $x^{3} - 3 x^{2} + x + 1$ are $a - b, a, a + b$ find $a$ and $b$ .
Answer Type	Text solution:1
Upvotes	150