Answer:
<h2><u>question 1</u></h2>
![n^{2} - 20n -96 = 0](https://tex.z-dn.net/?f=n%5E%7B2%7D%20-%2020n%20-96%20%3D%200)
use product and sum method
product = -96
sum = -20
numbers needed = ( -24 , 4)
n - 24 = 0
n + 4 = 0
hence <u>n = 24 and n = -4 </u>
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<h2><u>Question 2 </u></h2>
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in the form ![ax^{2} +bx +c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%20%2Bbx%20%2Bc%20%3D%200)
= ![x^{2} +12x - 48](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B12x%20-%2048)
make use of the formula :
![\frac{-b+-\sqrt{b^{2} -4ac} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E%7B2%7D%20-4ac%7D%20%7D%7B2a%7D)
replace values to make 2 equations :
1.
= 3.17
2.
= -15.2
hence <u>x = 3.17 and x = -15.2</u>
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<h2><u>Question 3 </u></h2>
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use product and sum method
product = 40
sum = -14
numbers needed = (-10 , -4)
x - 10 = 0
x - 4 = 0
hence<u> x = 10 and x = 4</u>
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<h2><u>Question 4 </u></h2>
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in the form ![ax^{2} +bx +c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%20%2Bbx%20%2Bc%20%3D%200)
this becomes ![5b^{2} -20b-18-7](https://tex.z-dn.net/?f=5b%5E%7B2%7D%20-20b-18-7)
= ![5b^{2} -20b-25](https://tex.z-dn.net/?f=5b%5E%7B2%7D%20-20b-25)
can simplify by 5
= ![b^{2} -4b-5 =0\\](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-4b-5%20%3D0%5C%5C)
use product and sum method
product = -5
sum = -4
numbers needed (-5 , 1)
b-5 = 0
b + 1 = 0
hence <u>b = 5 and b = -1</u>