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find a quadratic equation with solutions 3 and (-5/2)

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3 Answers

+3 and -5/2 are the roots of the equation.

 

this means that the quadratic equation has factors

 

(x-3)((x+5/2) = 0

 

relatively straightforward to FOIL thes binomial factors to get

 

x^2 + (5/2 x - 3x) -15/2 = 0

 

combine like terms (in the parentheses) to get

 

x^2 -(1/2)x -15/2 = 0

The roots of a quadratic equation are of the form:

               x + r1  =  0       and  x + r2  =  0

In this case, we have 

              x - 3  =  0      and      x + 5/2  = 0

To find a quadratic equation that satisfies those roots, multiply the two terms together:

           (x - 3)(x + 5/2)  = 0

           x2 - (1/2)x - 15/2  = 0

To eliminate the fraction, multiply through by 2:

          2x2 - x - 15  =  0

You can check this by factoring, or by using the quadratic formula.

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