Find the value of m so that the quadratic equation `mx(5x-6)=0` has two equal roots.

Options

A. 1
B. -1
C. 0
D. None

Explanation

To find the value of \( m \) such that the quadratic equation \( mx(5x - 6) = 0 \) has two equal roots, we can follow these steps:

### Step 1: Rewrite the equation
The given equation is:
\[ mx(5x - 6) = 0 \]
This can be expanded to:
\[ 5mx^2 - 6mx = 0 \]

### Step 2: Identify coefficients
From the expanded form \( 5mx^2 - 6mx = 0 \), we can identify the coefficients:
- \( a = 5m \)
- \( b = -6m \)
- \( c = 0 \)

### Step 3: Condition for equal roots
For a quadratic equation \( ax^2 + bx + c = 0 \) to have two equal roots, the discriminant \( D \) must be equal to zero. The discriminant is given by:
\[ D = b^2 - 4ac \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ D = (-6m)^2 - 4(5m)(0) \]
This simplifies to:
\[ D = 36m^2 - 0 = 36m^2 \]

### Step 4: Set the discriminant to zero
To find the value of \( m \) for which the roots are equal, we set the discriminant to zero:
\[ 36m^2 = 0 \]

### Step 5: Solve for \( m \)
Solving the equation \( 36m^2 = 0 \):
\[ m^2 = 0 \]
Taking the square root of both sides gives:
\[ m = 0 \]

### Conclusion
Thus, the value of \( m \) such that the quadratic equation \( mx(5x - 6) = 0 \) has two equal roots is:
\[ \boxed{0} \]