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When given the quadratic equation with integer roots: mx^2 - (m-2)x + m - 3 = 0 

What's the value of integer parameter m? And what are the integer roots?

 

edit: thank you so much!!

hearts123  Oct 19, 2018
edited by hearts123  Oct 20, 2018
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The discriminant  is

(m - 2)^2  - 4m (m - 3)

To have multiple roots....this must be a perfect square > 0

 

(m - 2)^2  - 4m (m - 3)  simplify

m^2 - 4m + 4 - 4m^2 + 12m

-3m^2 + 8m + 4

 

Graphing this.....it is only > 0   when the integer values for m  =    0, 1, 2 or 3

There are two values for m that produce a perfect square

When m  = 1.....the perfect square is 9

When m = 3, the perfect square is 1

 

So....one possible quadratic is

x^2 + x - 2    factoring we have (x + 2) (x - 1)  and the roots are  -2 and 1

 

The other possible quadratic is

3x^2  - x     factor   x (3x - 1)   and the roots are  0 and 1/3

However....we require integer roots...so

 

x^2 + x - 2  is the quadratic     and m = 1

 

 

cool cool cool

CPhill  Oct 20, 2018

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