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If α, β and γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:
- a)- 13/2
- b)- 1/2
- c)-3
- d)3
Correct answer is option 'C'. Can you explain this answer?
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If α, βand γ are the zeroes of the polynomial 2x3 + x...
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If α, βand γ are the zeroes of the polynomial 2x3 + x...
Understanding the Polynomial and its Roots
The given polynomial is 2x^3 + x^2 - 13x + 6. The roots of this polynomial are denoted as α, β, and γ. We need to find the product of the roots, αβγ.
Applying Vieta's Formulas
Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. For a cubic polynomial of the form ax^3 + bx^2 + cx + d, the relationships are:
- α + β + γ = -b/a
- αβ + βγ + γα = c/a
- αβγ = -d/a
Here, a = 2, b = 1, c = -13, and d = 6.
Finding the Product of the Roots
To find αβγ, we apply the third formula:
- αβγ = -d/a
Substituting the values:
- d = 6
- a = 2
Thus,
- αβγ = -6/2 = -3
Conclusion
The product of the roots α, β, and γ is -3. Therefore, the correct answer is option 'C', which is -3.
This calculation aligns with Vieta's relations, confirming that the product of the roots for the polynomial 2x^3 + x^2 - 13x + 6 indeed equals -3.
The given polynomial is 2x^3 + x^2 - 13x + 6. The roots of this polynomial are denoted as α, β, and γ. We need to find the product of the roots, αβγ.
Applying Vieta's Formulas
Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. For a cubic polynomial of the form ax^3 + bx^2 + cx + d, the relationships are:
- α + β + γ = -b/a
- αβ + βγ + γα = c/a
- αβγ = -d/a
Here, a = 2, b = 1, c = -13, and d = 6.
Finding the Product of the Roots
To find αβγ, we apply the third formula:
- αβγ = -d/a
Substituting the values:
- d = 6
- a = 2
Thus,
- αβγ = -6/2 = -3
Conclusion
The product of the roots α, β, and γ is -3. Therefore, the correct answer is option 'C', which is -3.
This calculation aligns with Vieta's relations, confirming that the product of the roots for the polynomial 2x^3 + x^2 - 13x + 6 indeed equals -3.
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If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer?.
If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, βand γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:a)- 13/2b)- 1/2c)-3d)3Correct answer is option 'C'. Can you explain this answer?.
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