# Polygon 42

Which polygon has 42 more diagonals than sides?

Result

n =  12

#### Solution:

$\dfrac12n (n-3) = n+42 \ \\ n^2 -5n -84 =0 \ \\ \ \\ a=1; b=-5; c=-84 \ \\ D = b^2 - 4ac = 5^2 - 4\cdot 1 \cdot (-84) = 361 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 5 \pm \sqrt{ 361 } }{ 2 } \ \\ n_{1,2} = \dfrac{ 5 \pm 19 }{ 2 } \ \\ n_{1,2} = 2.5 \pm 9.5 \ \\ n_{1} = 12 \ \\ n_{2} = -7 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -12) (n +7) = 0 \ \\ \ \\ n>0 \ \\ n = 12$

Checkout calculation with our calculator of quadratic equations.

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### Following knowledge from mathematics are needed to solve this word math problem:

Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

1. Boxes 200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
2. Pears Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
3. Ravens On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree?
4. Diagonals What x-gon has 54 diagonals?
5. Water reservoir The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
6. Fifth of the number The fifth of the number is by 24 less than that number. What is the number?
7. Roots Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
8. Equation Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
9. Fraction For what x expression ? equals zero? Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
11. Solve 3 Solve quadratic equation: (6n+1) (4n-1) = 3n2
12. Discriminant Determine the discriminant of the equation: ?
13. EQ2 Solve quadratic equation: ? Product of two numbers is 900. If we increase lowest number by 2 then product will increase by 150. Determine both numbers. Solve given equation with reciprocal member: a-6/a+10=4/8 Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?