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

Question 619186: If one zero of polynomial 5z2+13z-p is reciprocal of the other then find p.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
For the quadratic equation

The product of the zeros is c/a.

For your expression, in this form, is:

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:

Inserting your "a" and "c" into c/a:

Since your zeros are reciprocals are reciprocals and since the product of any reciprocals is always a 1, c/a must be 1:

Now we just solve this for p. Multiplying each side by 5:

Multiplying (or dividing) both sides by -1:

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