If $2,2$ are the roots of $x^2+px+b=0$ and $1,4$ are the roots of $x^2+ax+q=0$, then roots of the equation $x^2+ax+b=0$ are

For the first equation, using the sum and product of roots formulas gives p equals negative 4 and b equals 4. For the second equation, using the same formulas gives a equals negative 5 and q equals 4. The new equation x squared plus ax plus b equals 0 becomes x squared minus 5x plus 4 equals 0, and its discriminant is 25 minus 16, which equals 9, a positive number, so the roots are real and distinct.

• Thanks
• Wrong explanation