If $8,2$ are the roots $\displaystyle x^{2}+ax+c=0$ and $3,3$ are the roots of $\displaystyle x^{2}+dx+b=0$ then the roots of the equation $\displaystyle x^{2}+ax+b=0$ are

For the first equation, x squared plus ax plus c equals 0, the sum of the roots 8 and 2 gives a equals -10, and their product gives c equals 16. For the second equation, x squared plus dx plus b equals 0, the sum of the roots 3 and 3 gives d equals -6, and their product gives b equals 9. Substituting a equals -10 and b equals 9 into the new equation x squared plus ax plus b equals 0 gives x squared minus 10x plus 9 equals 0. Factoring this quadratic yields (x minus 1)(x minus 9) equals 0, so the roots are 1 and 9.

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