Questions: t^2-3t-10

Solution Steps

To solve the quadratic equation $t^2 - 3t - 10 = 0$, we can use the quadratic formula $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -3$, and $c = -10$.

We start with the quadratic equation given by

$$t^2 - 3t - 10 = 0$$

The discriminant $D$ is calculated using the formula

$$D = b^2 - 4ac$$

Substituting $a = 1$, $b = -3$, and $c = -10$:

$$D = (-3)^2 - 4 \cdot 1 \cdot (-10) = 9 + 40 = 49$$

Using the quadratic formula

$$t = \frac{-b \pm \sqrt{D}}{2a}$$

we can find the two solutions:

1. For $t_1$:

$$t_1 = \frac{-(-3) + \sqrt{49}}{2 \cdot 1} = \frac{3 + 7}{2} = \frac{10}{2} = 5.0$$

2. For $t_2$:

$$t_2 = \frac{-(-3) - \sqrt{49}}{2 \cdot 1} = \frac{3 - 7}{2} = \frac{-4}{2} = -2.0$$

Final Answer