(t+(8)/(3))(t+b)=0 In the given equation, b is a constant. If -(8)/(3) and (13)/(3) are solutions to the equation, then what is the value of b ?

Identify roots and factors: Identify the roots of the equation and relate them to the factors. Given roots: t = -8/3 and t = -13/3. The equation can be factored as (t + 8/3)(t + b) = 0. Thus, one factor is t + 8/3, and the other is t + b.Match roots to factors: Match the roots to the factors. Since t + 8/3 = 0 when t = -8/3, the other root, t = -13/3, must satisfy t + b = 0. So, set t + b = 0 and substitute t = -13/3: -13/3 + b = 0.Solve for b: Solve for b. -13/3 + b = 0 b = 13/3.

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$(t+\frac{8}{3})(t+b)=0$ $\newline$ In the given equation, $b$ is a constant. $\newline$ If $-\frac{8}{3}$ and $\frac{13}{3}$ are solutions to the equation, then what is the value of $b$ ?

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Algebra 1

Multiplication with rational exponents

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(t+\frac{8}{3})(t+b)=0

\newline

In the given equation,

b

is a constant.

\newline

-\frac{8}{3}

and

\frac{13}{3}

are solutions to the equation, then what is the value of

b

Identify roots and factors: Identify the roots of the equation and relate them to the factors. $\newline$ Given roots: $t = -\frac{8}{3}$ and $t = -\frac{13}{3}$ . $\newline$ The equation can be factored as $(t + \frac{8}{3})(t + b) = 0$ . $\newline$ Thus, one factor is $t + \frac{8}{3}$ , and the other is $t + b$ .
Match roots to factors: Match the roots to the factors. $\newline$ Since $t + \frac{8}{3} = 0$ when $t = -\frac{8}{3}$ , the other root, $t = -\frac{13}{3}$ , must satisfy $t + b = 0$ . $\newline$ So, set $t + b = 0$ and substitute $t = -\frac{13}{3}$ : $\newline$ $-\frac{13}{3} + b = 0$ .
Solve for b: Solve for b. $\newline$ $-\frac{13}{3} + b = 0$ $\newline$ $b = \frac{13}{3}$ .