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  • Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (iii) 2x ^2 - 6x + 3 = 0

Q1.    Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

                (iii)    2x^2 - 6x + 3 = 0

Answers (1)

The value of the discriminant 

b^2-4ac=(-6)^2-4\times2\times3=12

The discriminant > 0. Therefore the given quadratic equation has two distinct real root

roots are

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-6\pm\sqrt{12}}{2\times2}=\frac{3}{2}\pm\frac{\sqrt{3}}{2}

So the roots are

\frac{3}{2}+\frac{\sqrt{3}}{2}, \frac{3}{2}-\frac{\sqrt{3}}{2}

 

Posted by

Safeer PP

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