Questions: t^2-3t-10

Transcript text: \(t^{2}-3 t-10\)

Solution

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 \( c = -10 \).

Step 1: Identify the Quadratic Equation

We start with the quadratic equation given by

\[ t^2 - 3t - 10 = 0 \]

Step 2: Calculate the Discriminant

The discriminant \( D \) is calculated using the formula

\[ D = b^2 - 4ac \]

Substituting \( a = 1 \), \( b = -3 \), and \( c = -10 \):

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

Step 3: Find the Roots

Using the quadratic formula

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

we can find the two solutions:

For \( t_1 \):

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

For \( t_2 \):

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

Final Answer

The solutions to the equation \( t^2 - 3t - 10 = 0 \) are

\[ \boxed{t_1 = 5.0} \]

and

\[ \boxed{t_2 = -2.0} \]

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Questions: t^2-3t-10

Solution

Solution Steps

Final Answer

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