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how to write quadratic equations that has integer coefficients

Algebra
Tutor: None Selected Time limit: 1 Day

how to write a quadratic equation that has interger coefficients and has as solutions the given pair of numbers -1/3 and -4.

Mar 28th, 2015

solution : 

This is the formula for finding quadratic equation when solutions or roots are given 

X2(sum of roots) + x(product of roots) =0 ---------------------1

-1/3  , -4  are the  given roots

Sum of roots = - 1/3  - 4 =( -1- 12)/3 = - 13/3

Product of roots =  - 1/3  x  - 4 = 4/3

Putting these values in the above equation formula  -------------1

We have :

X2 (- 13/3) + x( 4/3) =0

Now we have same denominators 3 so, we can simplify like this :

-  13 X2 + 4x = 0 x3 =0

Or  13 X2 – 4x =0  taking ‘ –‘ as common 

Therefor the required  quadratic equation  is   13 X2 – 4x =0   

thanks

Mar 30th, 2015

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