It may appear that there is only one factor in the next example. Remember, however, that
means
.
Solve:
.
Solution
Rewrite the left side as a product.
Use the Zero Product Property and
set each factor to 0.
Solve the equations.
When a solution repeats, we call it
a double root.
Check your answer.
This image shows the steps for solving the equation (y – 8) squared = 0. The first step is to write the left hand side as a product, (y – 8)(y – 8) = 0. The next step is using the zero product property and set each factor equal to 0, y – 8 = 0 and y – 8 -= 0. Solve both equations, y = 8 and y = 8. When the solution repeats, it is a double root. Finally, check the solution by substituting back into the original equation.
Each of the equations we have solved in this section so far had one side in factored form. In order to use the Zero Product Property, the quadratic equation must be factored, with zero on one side. So we be sure to start with the quadratic equation in standard form,
. Then we factor the expression on the left.
Before we factor, we must make sure the quadratic equation is in standard form.
Solve:
.
Solution
Write the quadratic equation in standard form.
Factor the quadratic expression.
Use the Zero Product Property
to set each factor to 0.
Solve each equation.
Check your answers.
This image shows the steps for solving the equation 2 y squared = 13 y + 45. The first step is writing the equation in standard quadratic form, 2 y squared – 13 y – 45 = 0. The second step is to factor the quadratic expression, (2 y + 5)(y – 9) = 0. The third step is to use the zero product property to set each factor equal to 0, 2 y + 5 = 0 or y – 9 = 0. Solve each equation, y = −5/2 or y = 9. Finally, check the answers by substituting them back into the original equation.
Use the Zero Product Property
to set each factor to 0.
Solve each equation.
Check your answers.
This image shows the steps for solving the equation 5 x squared – 13 x = 7 x. The first step is writing the equation in standard quadratic form, 5 x squared – 20 x = 0. The second step is to factor the quadratic expression, 5 x(x – 4)= 0. The third step is to use the zero product property to set each factor equal to 0, 5 x = 0 or x − 4 = 0. Solve each equation, x = 0 or x = 4. Finally, check the answers by substituting them back into the original equation.
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
