# pre-calculus

posted by .

let f(x)=x^2 -(a^2 + 2a)x + 2a^3, where 0<a<2. for which value of a will the distance between the x-ints. of f be a maximum?

• pre-calculus -

using the quadratic formula, the discriminant is

(a^2+2a)^2 - 8a^3
= a^2((a+2)^2 - 8a)
= a^2(a-2)^2

So, we see that

x = ((a^2+2a) ± a(a-2))/2
= a^2 or 2a

so, if the roots are a^2 and 2a, the separation is 2a-a^2. When is that a maximum? When a=1.

## Similar Questions

1. ### pre-calculus

An open box is made from a square piece of material 36 inches on a side by cutting equal squares from the corners and turning up the sides. Use your calculator to find the maximum volume this box can hold. I got the equation 4x^3-36x^2+1296x …
2. ### calculus

what is the maximum distance between f and g when f(x)=1/2x^2 and g(x)=1/16x^4-1/2x^2 on closed interval [0,4]
3. ### College Algebra

so i am suppose to to find the max value attained by… g(x) = -3x2 - 24x - 18. but my teacher said "There is a difference between determining the maximum value and naming the location of the maximum value." what does that mean?
4. ### college Algebra

so i am suppose to to find the max value attained by… g(x) = -3x2 - 24x - 18. but my teacher said "There is a difference between determining the maximum value and naming the location of the maximum value." what does that mean?
5. ### Pre-Calculus

Find the maximum value, and where it occurs for eAch function. G(x)= (square root -x^2+4x+12)
6. ### Pre-Calculus

Find the maximum value of the function for the polygonal convex set determinded by the given system of inequalities. 8x + 2y > 36 –3x + 6y < 27 –7x + 5y > –18 f(x, y) = 9x + 5y
7. ### Pre-Calculus

Determine a quadratic function with this set of characteristics. x-intercepts of 2 and 7 and maximum value of 25 ( How would I find the x-coordinate for the vertex?
8. ### Pre-Calculus

Given: r = 4/(-2-6sinθ) What is the distance between the pole and the directrix?
9. ### pre calculus

what is the distance between the pole and the directrix of r = 4/-2-6sintheta
10. ### Calculus

If y = 18 - 3x, what is the maximum value of the product 2xy?

More Similar Questions