Question

Find the quadratic equation whose roots are 1/2 and -1/3​

Answer 1

`\begin{cases} x = \cfrac{1}{2} \implies 2x=1&\implies 2x-1=0\\[1em] x = -\cfrac{1}{3}\implies 3x=-1&\implies 3x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 2x -1 )( 3x +1 ) = \stackrel{0}{y}}\hspace{3em}\stackrel{\textit{now, we're assuming that}}{a=1}\qquad 1( 2x -1 )( 3x +1 ) =y \\\\\\ \stackrel{ F~O~I~L }{( 2x -1 )( 3x +1 )} =y\implies \boxed{6x^2-x-1=y}`