document.write( "Question 992267: Construct the quadratic equation in the form az2+bz+c =0 having the following solutions. Find the coefficients a, band c for each equation.
\n" ); document.write( "(a) \r
\n" ); document.write( "\n" ); document.write( "(a) z=7, z=−2.\r
\n" ); document.write( "\n" ); document.write( "___ z2+ ___ z+ ___ =0
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "(b) z=−3+4i, z=−3−4i.\r
\n" ); document.write( "\n" ); document.write( "___ z2+ ___ z+ ___ =0 \n" ); document.write( "

Algebra.Com's Answer #611898 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You cannot construct THE quadratic equation knowing only two points on the curve, in this case the two zeros or x-intercepts. In the case of your first example, you know that one factor of the quadratic trinomial is

and another factor is

. But there could also be some real number

such that the complete factorization of the trinomial would be

and the family of quadratic equations related in that they would all have the same roots would be

. Had the question asked you to construct A quadratic equation, that would have been a different story.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it\r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( "

\n" );