Find the quadratic equations of the following:
1. -2 and 3
2. 1/2 and 1
3. +√5 and -√5
Solutions:
1. -2 and 3
Let x= -2 and x= 3
X+2=0 and x-3=0
Put the two equations into two different brackets and equate all to 0
(X+2)(X-3)=0
Expand brackets(remove brackets by multiplying every term in the first bracket by each term in the second bracket)
X(X-3)+2(X-3)=0
x² -3x + 2x -6=0
x² - x - 6=0
2. ½ and 1
Let x=½ and x=1
x-½=0 and x-1=0
To eliminate the fraction in the first equation, multiply by 2
2x-1=0 and x-1=0
(2x-1)(x-1)=0
Expand
2x(x-1)-1(x-1)=0
2x² -2x-x+1=0
2x²-3x+1=0
3. +√5 and -√5
Let x=+√5 and x=-√5
x-√5=0 and x+√5=0
(x-√5)(x+√5)=0
Expand
x(x+√5)-√5(x+√5)=0
x²+x√5-x√5-5=0
x²-5=0
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