Question

Write the quadratic equation whose roots are 5 and 6 with leading coefficient of 3.

Answer 1

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:

`\begin{gathered} x=5,x=6 \\ \text{factors would be} \\ x-5,x-6 \end{gathered}`

The quadratic equation would be

`\begin{gathered} 3*(x-5)*(x-6) \\ =3*(x(x-6)-5(x-6)) \\ =3*(x^2-6x-5x+30) \end{gathered}`
`\begin{gathered} =3*(x^2-11x+30) \\ =3x^2-33x+90 \end{gathered}`

Hence, the quadratic equation is 3x²-33x+90