Given the roots of a quadratic equation as 5 and 6 with a leading coefficient of 3
To get the quadratic equation, we would find the two factors of the quadratic equation and multiply the factors with the leading coefficient as shown below:
[tex]\begin{gathered} x=5,x=6 \\ \text{factors would be} \\ x-5,x-6 \end{gathered}[/tex]The quadratic equation would be
[tex]\begin{gathered} 3\times(x-5)\times(x-6) \\ =3\times(x(x-6)-5(x-6)) \\ =3\times(x^2-6x-5x+30) \end{gathered}[/tex][tex]\begin{gathered} =3\times(x^2-11x+30) \\ =3x^2-33x+90 \end{gathered}[/tex]Hence, the quadratic equation is 3x²-33x+90
