Quadratic Equation

[burty1]

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!!

[gull]

Hint 1: Try using basic physics equations.

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

[jay_shark]

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 .

[Fels krone]

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

[Siegmund]

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.

[johnnyrocket]

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

[burty1]

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