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lara [203]
3 years ago
7

When the solutions are going to be complex, which methods can be used to solve quadratic equations?

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
7 0
You could complete the square to state the vertex. 
You could use the quadratic equation to find the roots (which are complex). 

Try an example that will require both.

y = x^2 + 2x + 5

Step One
Get the graph. That's included below.

Step Two
Provide the steps for completing the square.
Note: we should get (-1,4)

y= (x^2 +2x ) + 5
y = (x^2 +2x + 1) + 5 - 1
y = (x +1)^2 + 4

The vertex is at (-1,4)

Step Three
Find the roots. Use the quadratic equation. Note that the graph shows us that the equation never crosses or touches the x axis. The roots are complex.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

a = 1
b = 2
c = 5

\text{x = }\dfrac{ -2 \pm \sqrt{2^{2} - 4*1*5 } }{2}
\text{x = }\dfrac{ -2 \pm \sqrt{4 - 20 } }{2}
\text{x = }\dfrac{ -2 \pm \sqrt{-16 } }{2}
\text{x = }\dfrac{ -2 \pm 4i }{2}
x = -1 +/- 2i

x1 = -1 + 2i
x2 = -1 - 2i And we are done.


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Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly.
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Answer: Correct two digit number= 24

Step-by-step explanation:

Let

x= tens digit (wrong one)

and y= zeroes digit

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Now according to the statement,

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Simplifying this we get

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If we take the x-z=1

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This leaves us with x-z=3

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Put z=2 in x=3+z , we get x=5

So the numbers become 10x+y= 54

and 10z+y= 24

Their sum is 54+24=78

Check

54²-24²= 2340 so it is correct.

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2 years ago
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