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11. Find a cubic polynomial whose zeros are α, β, g such that α + β + γ= 6, αβ + βγ + gα = -1 and αβγ = -30.
  • a)
    x3 − 6x2− x +30
  • b)
    x3 + 6x2+ x −30
  • c)
    x3 −x2− 6 x +30
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
11. Find a cubic polynomial whose zeros are α, β, g such th...
Given α + β + γ = 6
αβ + βγ + γα = -1
αβγ = -30
The cubic polynomial is
P(x) = x3 - (α + β + γ)x2 + (αβ + βγ + γα)x - αβγ
= x3 - 6x2 - x - (-30)
(substituting the given values)
= x3 - 6x2 - x + 30
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Community Answer
11. Find a cubic polynomial whose zeros are α, β, g such th...
To find a cubic polynomial with zeros -2, 0, and 3, we can use the fact that if a polynomial has a zero at a certain value, then it must have a factor of (x - zero).

So, for the given zeros, the factors are: (x - (-2)), (x - 0), and (x - 3).

Simplifying these factors, we get: (x + 2), x, and (x - 3).

To find the cubic polynomial, we multiply these factors together:

(x + 2)(x)(x - 3)

Expanding this expression, we get:

(x^2 + 2x)(x - 3)

Now, we multiply each term in the first expression by each term in the second expression:

x^2(x - 3) + 2x(x - 3)

Expanding further, we get:

x^3 - 3x^2 + 2x^2 - 6x

Combining like terms, we have:

x^3 - x^2 - 6x

Therefore, the cubic polynomial with zeros -2, 0, and 3 is:

f(x) = x^3 - x^2 - 6x
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11. Find a cubic polynomial whose zeros are α, β, g such that α + β + γ= 6, αβ + βγ + gα = -1 and αβγ = -30.a)x3 − 6x2− x +30b)x3 + 6x2+ x −30c)x3 −x2− 6 x +30d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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