Question

If the zeroes of a quadratic polynomial \( 3x^2 - kx + 12 \) are equal, then find the value of \( k \).

Hint:

The condition for equal roots of a quadratic equation is that the discriminant should be zero. Use the discriminant formula to find the value of the coefficient.

Answer 1

Step 1: Use the condition for equal roots.}
For a quadratic polynomial \( ax^2 + bx + c \), the roots are equal when the discriminant (\( \Delta \)) is zero. The discriminant is given by: \[ \Delta = b^2 - 4ac \]
Step 2: Identify values of \( a \), \( b \), and \( c \).}
For the polynomial \( 3x^2 - kx + 12 \), we have: - \( a = 3 \)
- \( b = -k \)
- \( c = 12 \)

Step 3: Set the discriminant to zero.}
Using the discriminant formula, we get: \[ \Delta = (-k)^2 - 4(3)(12) \] \[ \Delta = k^2 - 144 \] Since the roots are equal, \( \Delta = 0 \), so: \[ k^2 - 144 = 0 \]
Step 4: Solve for \( k \).}
Solving for \( k \): \[ k^2 = 144 \] \[ k = \pm 12 \] % Final Answer Final Answer:
The value of \( k \) is \( \pm 12 \).