Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $t$ . $\newline$ $t(t - 1) = 0$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $t =$ _ or $t =$ _

View step-by-step help

View step-by-step help

Solve a quadratic equation using the zero product property

Full solution

Q. Solve for

t

.

\newline

t(t - 1) = 0

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

t =

_____ or

t =

_____

Apply Zero Product Property: We are given the equation $t(t - 1) = 0$ . To solve for $t$ , we can apply the zero product property, which states that if the product of two factors is $0$ , then at least one of the factors must be $0$ .
Set Equations Equal to Zero: Set each factor equal to zero separately. This gives us two equations to solve: $\newline$ $1$ . $t = 0$ $\newline$ $2$ . $t - 1 = 0$
Solve for $t = 0$ : Solve the first equation: $\newline$ $t = 0$ $\newline$ This is already solved, so we have our first value of $t$ .
Solve for $t = 1$ : Solve the second equation: $\newline$ $t − 1 = 0$ $\newline$ Add $1$ to both sides to isolate $t$ : $\newline$ $t = 1$ $\newline$ Now we have our second value of $t$ .

More problems from Solve a quadratic equation using the zero product property

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 7 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 5 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 5 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 5 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 4 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant