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The equation: ax^2+bx+c=0 may have two real solutions, one real solution, or a conjugate complex pair of solutions. Assuming there are two real solutions, and a > 0, the smaller is x= ________. (This is the celebrated quadratic formula) Find the smaller solution.

Sagot :

Given:

The quadratic equation,

[tex]ax^2+bx+c=0[/tex]

As the given equation has two real solution and a>0.

The solution is given by the formula,

[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{For a<0 the value for }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ will be positive and it will give the greater value.} \\ \text{ For a>0 it will give the value obtained will always be smaller.} \end{gathered}[/tex]

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