To solve this problem you must apply the proccedure shown below:
1. You have that:
- T<span>he equation d=1/2(n(n-3)) gives the number of diagonals for the polygon.
- The polygon that has 65 diagonals..
2. When you clear n, you obtain:
d=n(n-3)/2
d=(n^2-3n)/2
2x65=n^2-3n
n^2-3n-130=0
3. When you solve the quadratic equation, you obtain:
n=13
Therefore, the answer is: 13 sides. </span>
Rational Roots Theorem states if a polynomial P (x) has rational roots then p/q is a root where p is a multiple of a0 and q of an. Moreover this polynomial has 3 roots, at most 3 which are positive and none of which are negative. Finding a root x0, you can use (x-x0) and long division to factor P (x) and find the other roots. Possible rational roots +/- {1,2,3,6,7,14,21}.
Namely 2,3,7 are the roots so it factors
(x-2)(x-3)(x-7)
Answer:
-3, 2
Step-by-step explanation:
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