Class 10 Exam > Class 10 Questions > A quadratic polynomial, whose zeroes are &nda...
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A quadratic polynomial, whose zeroes are –3 and 4, is
- a)x2 – x + 12
- b)x2 + x + 12
- c)(x2/2) – (x/2) – 6
- d)2x2 + 2x – 24
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 &ndash...
Understanding Quadratic Polynomials
A quadratic polynomial can be expressed in the form of ax² + bx + c, where a, b, and c are constants. The roots (or zeroes) of the polynomial are the values of x that make the polynomial equal to zero.
Finding the Polynomial with Given Zeroes
Given the zeroes -3 and 4, we can use the fact that if p and q are the zeroes of a quadratic polynomial, it can be expressed as:
- P(x) = a(x - p)(x - q)
Substituting the zeroes:
- P(x) = a(x + 3)(x - 4)
Expanding the Expression
Now, let's expand this expression:
1. P(x) = a[(x + 3)(x - 4)]
2. P(x) = a[x² - 4x + 3x - 12]
3. P(x) = a[x² - x - 12]
Choosing the Value of a
To find a suitable form, we can choose a = 1 for simplicity, giving:
- P(x) = x² - x - 12
However, we need to check the options presented.
Evaluating the Options
- Option a: x² - x + 12 (Incorrect, does not match)
- Option b: x² + x + 12 (Incorrect, does not match)
- Option c: (x²/2) - (x/2) - 6 (Let’s analyze)
- Option d: 2x² + 2x - 24 (Incorrect, does not match)
Verifying Option C
To verify option c:
1. Multiply the entire expression by 2 to eliminate the fraction:
- 2[(x²/2) - (x/2) - 6] = x² - x - 12
This matches our previously derived polynomial.
Conclusion
Thus, the correct answer is option c: (x²/2) - (x/2) - 6, as it is equivalent to the polynomial derived from the given zeroes -3 and 4.
A quadratic polynomial can be expressed in the form of ax² + bx + c, where a, b, and c are constants. The roots (or zeroes) of the polynomial are the values of x that make the polynomial equal to zero.
Finding the Polynomial with Given Zeroes
Given the zeroes -3 and 4, we can use the fact that if p and q are the zeroes of a quadratic polynomial, it can be expressed as:
- P(x) = a(x - p)(x - q)
Substituting the zeroes:
- P(x) = a(x + 3)(x - 4)
Expanding the Expression
Now, let's expand this expression:
1. P(x) = a[(x + 3)(x - 4)]
2. P(x) = a[x² - 4x + 3x - 12]
3. P(x) = a[x² - x - 12]
Choosing the Value of a
To find a suitable form, we can choose a = 1 for simplicity, giving:
- P(x) = x² - x - 12
However, we need to check the options presented.
Evaluating the Options
- Option a: x² - x + 12 (Incorrect, does not match)
- Option b: x² + x + 12 (Incorrect, does not match)
- Option c: (x²/2) - (x/2) - 6 (Let’s analyze)
- Option d: 2x² + 2x - 24 (Incorrect, does not match)
Verifying Option C
To verify option c:
1. Multiply the entire expression by 2 to eliminate the fraction:
- 2[(x²/2) - (x/2) - 6] = x² - x - 12
This matches our previously derived polynomial.
Conclusion
Thus, the correct answer is option c: (x²/2) - (x/2) - 6, as it is equivalent to the polynomial derived from the given zeroes -3 and 4.
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Community Answer
A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 &ndash...
A quadratic polynomial in terms of the
zeroes
α and β is given byx2 - (sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α + β) x + αβ
Now,
Given that zeroes of a quadratic polynomial are -3 and 4
Let α = -3 and β = 4
Therefore, substituting the value α = -3 and β = 4 inf(x) = x2 -(α + β) x + αβ, we get
f(x) = x2 - ( -3 + 4) x +(-3)(4)
= x2 - x - 12, which is equal to (x2/2) – (x/2) – 6
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A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct 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 A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct 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 A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct answer is option 'C'. Can you explain this answer?.
A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct 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 A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct 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 A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct answer is option 'C'. Can you explain this answer?.
Solutions for A quadratic polynomial, whose zeroes are –3 and 4, isa)x2 – x + 12b)x2+ x + 12c)(x2/2) – (x/2) – 6d)2x2 + 2x – 24Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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