Quadratic Equation
 

I'm taking a class and cannot come up with an answer to this question...any help would be appreciated...

Come up with a real life situation modeled by (X-3)(X-4) = 0.

Help!!

Re: Quadratic Equation
 

Hint 1: Try using basic physics equations.

Hint 2: x^2 - 7x + 12 = 0

Re: Quadratic Equation
 

Replace the x with a t .

V(t) = (t-3)(t-4) where t= time .
V(t) is the velocity function with respect to time . If you're interested in time t for when the velocity of some moving object is 0 then you find the roots . The displacement function is S(t) such that S'(t)=V(t) .

It's obvious that between t=3 and t=4 there is negative velocity and for t>4 , the velocity becomes positive .

Re: Quadratic Equation
 

You could model a spring-mass damper system. Assuming the damping coefficient was related to the mass velocity; and there was no other forces acting on the mass. Weight can be ignored if system starts from equilibrium.

From F = ma

kx + bx' = mx"

The characteristic eqn would become

x^2 - 7x + 12 = 0

mass m = 1
damping coefficient b = -7
spring constant k = 12

Re: Quadratic Equation
 

If you want a non-physics application... consider frames for different sizes of pictures, with the photo placed inside a matte that is 2" wide above and below the picture and 1 1/2" wide to either side of it... (X-3)(X-4) is the area of the largest matted picture that can be displayed in an X by X frame.

Re: Quadratic Equation
 

well since the equation forms a parabolic graph, you can do something like a person is standing on top of a 12 foot roof, he throws a ball upwards, this equation would model this well since the equation of the flight of the ball would be parabolic and this would start at this height. Hope this helps

Re: Quadratic Equation
 

As expected...people on this forum are intelligent and fast and courteous...thanks for the responses...