Question

If A={x^2-5x+6=0,x€n} and B={3,4,5} find A×B

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Answer 1

Answer:

The given quadratic equation is x

2

−5x+6=0.

Let y=x

2

−5x+6, when we substitute different values of x in the equation y=x

2

−5x+6 then value of y changes accordingly.

When x=0 then

y=(0)

2

−(5×0)+6=0−0+6=6

The point is (0,6)

When x=2 then

y=(2)

2

−(5×2)+6=4−10+6=10−10=0

The point is (2,0)

When x=3 then

y=(3)

2

−(5×3)+6=9−15+6=15−15=0

The point is (3,0)

Therefore, the coordinates are (0,6), (2,0) and (3,0) and the graph of the quadratic equation y=x

2

−5x+6 is as shown above.

Hence, from above graph, we get that x=2 or x=3.