Question

Form the quadratic equation from the roots given below.

\[\frac{1}{2}, - \frac{1}{2}\]

Answer 1

\[\frac{1}{2}, - \frac{1}{2}\] 

Sum of roots =\[\frac{1}{2} + \left( - \frac{1}{2} \right) = 0\] 

Product of roots = \[\frac{1}{2} \times \left( \frac{- 1}{2} \right) = \frac{- 1}{4}\] 

The general form of the quadratic equation is \[x^2 - \left( \text{ Sum of roots } \right)x + \text{ Product of roots } = 0\] 

So, the quadratic equation obtained is \[x^2 - \left( 0 \right)x + \left( \frac{- 1}{4} \right) = 0\] 

\[\Rightarrow x^2 - \frac{1}{4} = 0\]