+0  
 
0
56
1
avatar

My main problem is that I dont know write this polynomial's function.

 Mar 8, 2021
 #1
avatar+32062 
+2

There are three turning points, so you have a fourth order polynomial.  It has roots at -5 and -1 (i..e. places where the function is zero.

 

Write the function as f(x) = -(x + 5)(x + 1)(x - a)(x - b)  where a and b are to be found (the initial negative sign is because the function goes to -infinity as x goes to +/- infinity)

 

When x = 0 we have f(0) = -25, so    -5*a*b = -25  ...(1)

 

There gradient of f is zero when x = -3, so differentiate f with respect to x and set the result equal to zero (with x = -3)

 

df/dx = -(4*x^3 + (18-3a-3b)*x^2 + (2ab-12a-12b+10)*x - 6ab - 5a -5b) 

 

so 4*(-3)^3 + (18 - 3a - 3b)*(-3)^2 + (2ab -12a -12b + 10)*(-3) -6ab - 5a -5b = 0   ...(2)

 

You now have two equations for the two unknowns a and b.

 

Can you take it from here?

 Mar 8, 2021
edited by Alan  Mar 8, 2021
edited by Alan  Mar 8, 2021

32 Online Users

avatar
avatar
avatar
avatar
avatar
avatar