Question

Draw the graph of y = x2

+3x + 2 and use it solve x2

+ 2x + 1 = 0

answer as soon as possible

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Answer 1

Answer:

First, let us form a table for y=x

2

+3x+2

x −4 −3 −2 −1 0 1 2 3

x

2

16 9 4 1 0 1 4 9

3x −12 −9 −6 −3 0 3 6 9

2 2 2 2 2 2 2 2 2

y 6 2 0 0 2 6 12 20

Plot the points (−4,6),(−3,2),(−2,0)),(1,6),(2,12) and (3,20)

Now, join the points by a smooth curve. The curve so obtained, is the graph of y=x

2

+3x+2.

Now, x

2

+2x+4=0

⇒ x

2

+3x+2−x+2=0

⇒ y=x−2 ∵ y=x

2

+3x+2

Thus the roots of x

2

+2x+4=0 are obtained from the points of intersection of

y=x−2 and y=x

2

+3x+2

Now, form the table for the line y=x−2

x −2 0 1 2

y=x−2 −4 −2 −1 0

The straight line y=x−2 does not intersect the curve y=x

2

+3x+2. Thus, x

2

+2x+4=0 has not real roots.

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