Answer:
question 1
[tex]n^{2} - 20n -96 = 0[/tex]
use product and sum method
product = -96
sum = -20
numbers needed = ( -24 , 4)
n - 24 = 0
n + 4 = 0
hence n = 24 and n = -4
Question 2
[tex]x^{2} + 12 x = 48[/tex]
in the form [tex]ax^{2} +bx +c = 0[/tex]
= [tex]x^{2} +12x - 48[/tex]
make use of the formula :
[tex]\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
replace values to make 2 equations :
1.[tex]\frac{-12+\sqrt{12^{2} -4*1*-48} }{2*1}[/tex] = 3.17
2.[tex]\frac{-12-\sqrt{12^{2} -4*1*-48} }{2*1}[/tex] = -15.2
hence x = 3.17 and x = -15.2
Question 3
[tex]x^{2} -14x+40=0[/tex]
use product and sum method
product = 40
sum = -14
numbers needed = (-10 , -4)
x - 10 = 0
x - 4 = 0
hence x = 10 and x = 4
Question 4
[tex]5b^{2} -20b-18 = 7[/tex]
in the form [tex]ax^{2} +bx +c = 0[/tex]
this becomes [tex]5b^{2} -20b-18-7[/tex]
= [tex]5b^{2} -20b-25[/tex]
can simplify by 5
= [tex]b^{2} -4b-5 =0\\[/tex]
use product and sum method
product = -5
sum = -4
numbers needed (-5 , 1)
b-5 = 0
b + 1 = 0
hence b = 5 and b = -1
