Question3) $12v^2 - 6v + 10 = 0$
Solve each equation with the quadratic formula

Studdy Solution
Apply the quadratic formula to find the solutions for $v$.
$$v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ $$v = \frac{-(-6) \pm \sqrt{-444}}{2 \times 12}$$ $$v = \frac{6 \pm \sqrt{-444}}{24}$$
Express the square root of the negative discriminant in terms of imaginary numbers:
$$\sqrt{-444} = \sqrt{444}i$$
Thus, the solutions are:
$$v = \frac{6 \pm \sqrt{444}i}{24}$$
Simplify further if possible:
$$v = \frac{6 \pm \sqrt{4 \times 111}i}{24}$$ $$v = \frac{6 \pm 2\sqrt{111}i}{24}$$ $$v = \frac{3 \pm \sqrt{111}i}{12}$$
The solutions for $v$ are:
$$v = \frac{3 + \sqrt{111}i}{12} \quad \text{and} \quad v = \frac{3 - \sqrt{111}i}{12}$$