Question:
The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is
The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is
Show Hint
Be careful with the signs when applying the formula \(-\frac{b}{a}\).
Since the coefficient of \(x\) is already \(-k\), the formula gives \(-(-k)/3 = k/3\).
A common mistake is to write \(-k/3 = 2\), which leads to an incorrect answer of \(-6\).
Since the coefficient of \(x\) is already \(-k\), the formula gives \(-(-k)/3 = k/3\).
A common mistake is to write \(-k/3 = 2\), which leads to an incorrect answer of \(-6\).
Updated On: Jun 25, 2026
- 2
- \(-6\)
- \(-2\)
- 6
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
This question belongs to the topic of Polynomials, specifically focusing on quadratic polynomials and the relationship between their coefficients and zeroes.
We are given a quadratic polynomial \(p(x) = 3x^2 - kx + 6\) where the coefficient of \(x\) contains an unknown parameter \(k\).
The sum of the zeroes of this polynomial is given as 2, and we need to solve for the value of \(k\).
Step 2: Key Formula or Approach:
For a standard quadratic polynomial of the form \(ax^2 + bx + c\), let the zeroes be \(\alpha\) and \(\beta\).
The relationship between the sum of the zeroes and the coefficients is given by: \[ \text{Sum of zeroes } (\alpha + \beta) = -\frac{\text{Coefficient of } x}{\text{Coefficient of } x^2} = -\frac{b}{a} \]
Step 3: Detailed Explanation:
1. Compare the given polynomial \(p(x) = 3x^2 - kx + 6\) with the standard form \(ax^2 + bx + c\):
- Coefficient of \(x^2\) is \(a = 3\)
- Coefficient of \(x\) is \(b = -k\)
- Constant term is \(c = 6\)
2. Using the relationship for the sum of zeroes: \[ \alpha + \beta = -\frac{b}{a} \] 3. Substitute the values of \(a\) and \(b\) into the formula: \[ \alpha + \beta = -\frac{-k}{3} = \frac{k}{3} \] 4. We are given that the sum of the zeroes is 2: \[ \frac{k}{3} = 2 \] 5. Solve for \(k\) by multiplying both sides by 3: \[ k = 2 \times 3 \] \[ k = 6 \]
Step 4: Final Answer:
The value of \(k\) for which the sum of the zeroes is 2 is determined to be 6.
Therefore, the correct option is (D).
This question belongs to the topic of Polynomials, specifically focusing on quadratic polynomials and the relationship between their coefficients and zeroes.
We are given a quadratic polynomial \(p(x) = 3x^2 - kx + 6\) where the coefficient of \(x\) contains an unknown parameter \(k\).
The sum of the zeroes of this polynomial is given as 2, and we need to solve for the value of \(k\).
Step 2: Key Formula or Approach:
For a standard quadratic polynomial of the form \(ax^2 + bx + c\), let the zeroes be \(\alpha\) and \(\beta\).
The relationship between the sum of the zeroes and the coefficients is given by: \[ \text{Sum of zeroes } (\alpha + \beta) = -\frac{\text{Coefficient of } x}{\text{Coefficient of } x^2} = -\frac{b}{a} \]
Step 3: Detailed Explanation:
1. Compare the given polynomial \(p(x) = 3x^2 - kx + 6\) with the standard form \(ax^2 + bx + c\):
- Coefficient of \(x^2\) is \(a = 3\)
- Coefficient of \(x\) is \(b = -k\)
- Constant term is \(c = 6\)
2. Using the relationship for the sum of zeroes: \[ \alpha + \beta = -\frac{b}{a} \] 3. Substitute the values of \(a\) and \(b\) into the formula: \[ \alpha + \beta = -\frac{-k}{3} = \frac{k}{3} \] 4. We are given that the sum of the zeroes is 2: \[ \frac{k}{3} = 2 \] 5. Solve for \(k\) by multiplying both sides by 3: \[ k = 2 \times 3 \] \[ k = 6 \]
Step 4: Final Answer:
The value of \(k\) for which the sum of the zeroes is 2 is determined to be 6.
Therefore, the correct option is (D).
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