Question

Part 1:
Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. Show your work to receive full credit.

0 = x2 + 5x + 6
0 = x2 + 4x + 4

Part 2:
Using complete sentences, answer the following questions about the two quadratic equations above.

Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 4x + 4 different from y = x2 + 5x + 6?

Answer 1

very easy. firstly x^2=\[x ^{2}\]
now your equation x^2+5x+6=0, we will solve by factorization althought we can also solve by quadratic formula i.e \[x=(-b \sqrt{b^2-4ac} )\div2a\] but we will solve by factorization because it is easy,
x^2+5x+6=0
x^2+2x+3x+6=0
x(x+2)+3(x+2)=0
(x+2)(x+3)=0
either x+2=0 or x+3=0
either x=-2 or x=-3

Answer 2

now 2nd equation x^2+4x+4 , we will factorize
x^2+2x+2x+4=0
x(x+2)+2(x+2)=0
(x+2)(x+2)=0
x+2=0 or x+2=0
x=-2, the main difference between two equations is this that the first equation gave 2 answers and both satisfied the equation but 2nd equation gave two same answer and they obviously satisfied the equation

Answer 3

these quadratic equation have something in common i.e they both can be solved by factorization and there is no need to apply quadratic formula