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Sum and Product of Roots

The document discusses finding quadratic equations given their roots. It shows that the sum of the roots is the coefficient of the linear term, and the product of the roots is the constant term. Examples are provided to illustrate this pattern.

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Irish Serdeña - Sigue
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350 views2 pages

Sum and Product of Roots

The document discusses finding quadratic equations given their roots. It shows that the sum of the roots is the coefficient of the linear term, and the product of the roots is the constant term. Examples are provided to illustrate this pattern.

Uploaded by

Irish Serdeña - Sigue
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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Sum and Product of the Roots Name:

We’ve seen how we can come up with a possible quadratic equation given its roots or solutions. For
example, if I know that a quadratic equation has roots 5 and -2, I could follow the process below:
x  5, x  2
x  5  0, x  2  0
( x  5)( x  2)  0
x 2  2 x  5 x  10  0
x 2  3 x  10  0
This is one possible quadratic equation with these roots.

Question: What’s another possible quadratic equation with these roots?_________________________

Question: How many different quadratic equations have these roots?____________________________

There is another way to find a quadratic equation given its roots that many people find useful. Look below
at the roots and the equations that have those roots. Can you discover the shortcut?

Roots possible quadratic equation with those roots


5 and  2 x 2  3 x  10  0
6 and 5 x 2  11x  30  0
 1 and  7 x 2  8x  7  0
 20 and 3 x 2  17 x  60  0
5 and 4 x 2  9 x  20  0
5 and  5 x 2  25  0

What pattern do you see?

Does the pattern or shortcut you discovered above work for these examples?

3 3
and  4x2  9  0
2 2

1
and  2 5x 2  9 x  2  0
5
2 1
and 9x2  9x  2  0
3 3
Let’s write down this shortcut.
Remember: We can find any quadratic equation that has these roots. So to make things a bit easier, let’s find
the quadratic equation with a  1 .

When a  1 , then b  ____________________________, and c  __________________________.

1) Given the roots below, write a quadratic equation with those roots.

a) 5 and  2 b)  5 and  2

2 1
c) 6 and 3 d) and
3 3

2) Given the sum of the roots and the product of the roots, write a quadratic equation.

a) sum  8, product  12 b) sum  8, product  12

4 3
c) sum  7, product  10 d) sum  , product 
7 49

3) Given the quadratic equations below, find the sum of the roots and the product of the roots.

a) x 2  9 x  8  0 b) x 2  x  7  0

c) 2 x 2  6 x  10  0 d) 3 x 2  3 x  11  0

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