Question

if the zeros of the polynomial x³-3x²+x+2 are a- b , a and a+ b , find the values of a and b.


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Answer 1

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Answer 2

Answer:

Given:-

→ p(x)= x³ -3x² +x+1

and the zeroes are

→ (a-b), a ,(a+b)

\alpha \: + \beta \: + \gamma = \frac{ - b}{a}α+β+γ=

a

−b

Here ,

→ a = 1

→ b = -3

→ c = 1

→ d = 1

→ a - b + a + a + b = -(-3)/1

→ 3a = 3

→ a = 3/3

→ a = 1.

Now,

\alpha \times \beta \times y = \frac{ - d}{a}α×β×y=

a

−d

→ (a - b) (a) (a+b) = -d/a

→ (a-b) (a+b) (a)= -1/1

→ a² - b² × a = -1

put the value of a in it

→ 1² - b² ×1 = -1

→ 1 - b² = -1

→ -b² = -1-1

→ -b² = -2

→ b = ±√2

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