Questions: -16 t^2 + 364 t

Transcript text: $-16 t^{2}+364 t$

Solution

Solution Steps

To solve the expression $-16t^2 + 364t$, we can factor out the greatest common factor from the terms. The greatest common factor here is 4t. After factoring, we can express the quadratic in its factored form.

Step 1: Factor the Expression

We start with the expression

\[ -16t^2 + 364t \]

To factor this expression, we identify the greatest common factor, which is $4t$. Thus, we can rewrite the expression as:

\[ -16t^2 + 364t = -4t(4t - 91) \]

Step 2: Identify the Roots

To find the roots of the factored expression, we set it equal to zero:

\[ -4t(4t - 91) = 0 \]

This gives us two equations to solve:

$ -4t = 0 $
$ 4t - 91 = 0 $

From the first equation, we find:

\[ t = 0 \]

From the second equation, we solve for $t$:

\[ 4t = 91 \implies t = \frac{91}{4} \]

Step 3: Summarize the Roots

The roots of the expression are:

\[ t = 0 \quad \text{and} \quad t = \frac{91}{4} \]

Final Answer

The roots of the expression are

\[ \boxed{t = 0} \quad \text{and} \quad \boxed{t = \frac{91}{4}} \]

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