1. ## 2 questions

1. Find all the values of H such that the equation 3x2-2x + H=O has imaginary roots.

2.When a Current, C flows through a given electrical circut, the power, W of the circuit can be determined by the formula W= 120C - 12C2. What amount of current supplies the maximum power. And what is the maximum power that can be delivered in this circuit.

the 2 after the c and X means squared sorry don't know how else to do it.
Thank ou

2. Originally Posted by key

1. Find all the values of H such that the equation 3x2-2x + H=O has imaginary roots.
we have imaginary roots when the discriminant is negative, that is, when $b^2 - 4ac = 4 - 12H < 0$

3. Originally Posted by key
2.When a Current, C flows through a given electrical circut, the power, W of the circuit can be determined by the formula W= 120C - 12C2. What amount of current supplies the maximum power. And what is the maximum power that can be delivered in this circuit.

the 2 after the c and X means squared sorry don't know how else to do it.
Thank ou
the formula for power is a downward opening parabola. find the vertex of the parabola. the "x"-value gives the current and the "y"-value gives the maximum power

1. For a parabola $f(x) = ax^2 + bx + c$ the vertex is given by: $\left( \frac {-b}{2a}, f \left( \frac {-b}{2a} \right) \right)$
so $\frac {-b}{2a}$ is the current and $f \left( \frac {-b}{2a}$ is the max power
2. Complete the square to get the quadratic in the form $W = a(C - h)^2 + k$
when in this form, the vertex is given by $(h,k)$
so $h$ is the current, and $k$ is the max power