SOLUTION: If one zero of polynomial 5z2+13z-p is reciprocal of the other then find p.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If one zero of polynomial 5z2+13z-p is reciprocal of the other then find p.      Log On


   

Question 619186: If one zero of polynomial 5z2+13z-p is reciprocal of the other then find p.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For the quadratic equation
ax%5E2%2Bbx%2Bc=+0
The product of the zeros is c/a.

For your expression, in this form, is:
5z%5E2%2B13z%2B%28-p%29
This makes your
a = 5
b = 13
c = -p

You are told that the zeros of your expression are reciprocals. Zeros of a polynomial are the values for the variable that make the polynomial equal to zero. IOW, they are soluti8ons to:
5z%5E2%2B13z%2B%28-p%29+=+0

Inserting your "a" and "c" into c/a:
%28-p%29%2F5
Since your zeros are reciprocals are reciprocals and since the product of any reciprocals is always a 1, c/a must be 1:
%28-p%29%2F5+=+1

Now we just solve this for p. Multiplying each side by 5:
-p+=+5
Multiplying (or dividing) both sides by -1:
p+=+-5