Given a quadratic equation with the leading coefficient of 1, factor it.
Find two numbers whose product equals
c and whose sum equals
b .
Use those numbers to write two factors of the form
where
k is one of the numbers found in step 1. Use the numbers exactly as they are. In other words, if the two numbers are 1 and
the factors are
Solve using the zero-product property by setting each factor equal to zero and solving for the variable.
Solving a quadratic equation by factoring when the leading coefficient is not 1
Factor and solve the equation:
To factor
we look for two numbers whose product equals
and whose sum equals 1. Begin by looking at the possible factors of
The last pair,
sums to 1, so these are the numbers. Note that only one pair of numbers will work. Then, write the factors.
To solve this equation, we use the zero-product property. Set each factor equal to zero and solve.
The two solutions are
and
We can see how the solutions relate to the graph in
[link] . The solutions are the
x- intercepts of
Using the zero-product property to solve a quadratic equation written as the difference of squares
Solve the difference of squares equation using the zero-product property:
Recognizing that the equation represents the difference of squares, we can write the two factors by taking the square root of each term, using a minus sign as the operator in one factor and a plus sign as the operator in the other. Solve using the zero-factor property.
Solving a quadratic equation by factoring when the leading coefficient is not 1
When the leading coefficient is not 1, we factor a quadratic equation using the method called grouping, which requires four terms. With the equation in standard form, let’s review the grouping procedures:
With the quadratic in standard form,
multiply
Find two numbers whose product equals
and whose sum equals
Rewrite the equation replacing the
term with two terms using the numbers found in step 1 as coefficients of
x.
Factor the first two terms and then factor the last two terms. The expressions in parentheses must be exactly the same to use grouping.
Factor out the expression in parentheses.
Set the expressions equal to zero and solve for the variable.
Questions & Answers
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?
