Question

The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is

• A. 2
• B. \(-6\)
• C. \(-2\)
• D. 6

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 \(-6\).

Answer 1

The Correct Option is D

Step 1: Identify the polynomial.
The polynomial is \(p(x) = 3x^2 - kx + 6\). Here \(a = 3\), \(b = -k\), \(c = 6\).
Step 2: Recall the relationship for sum of zeroes.
For a quadratic \(ax^2 + bx + c\), the sum of zeroes \(= -\frac{b}{a}\).
Step 3: Apply the formula.
Sum of zeroes \(= -\frac{-k}{3} = \frac{k}{3}\).
Step 4: Set up the equation.
We are told the sum of zeroes is 2: \(\frac{k}{3} = 2\).
Step 5: Solve for k.
\(k = 2 \times 3 = 6\).
Step 6: Select the correct option.
\(k = 6\), which is option 4.
\[ \boxed{k = 6} \]