Q 64. The solution of the equation: 6е2+3e* = 0 is x= Ops: A. 4 B. No Solution C. log4 D. e^2

1. Break Down the Problem

We have the equation $6e^2 + 3e^* = 0$. To solve for $x$, we need to isolate $e^*$.

2. Relevant Concepts

The equation resembles a quadratic form. We can factor out the common term if possible, and we can use properties of equations to solve for the unknown.

3. Analysis and Detail

1. Rearranging the equation: $6e^2 + 3e^* = 0$ This means we can factor out the common term: $3(e^* + 2e^2) = 0$ Thus, we can set each factor to zero: $3 = 0 \quad \text{(not applicable)}, \quad e^* + 2e^2 = 0$

2. Isolating $e^*$: $e^* = -2e^2$

4. Verify and Summarize

The expression $e^* = -2e^2$ does not give us a value for $x$ in terms of real numbers since $e$ (approximately $2.718$) is always positive, and therefore $-2e^2$ cannot be equal to any real number.

Final Answer

Thus, the correct option is: B. No Solution