Given:
The roots of a quadratic equation are 6 and 2.
Explanation:
The factors of a quadratic with roots 6 and 2 are,
[tex](x-6)\text{ and (x}-2)[/tex]The quadratic equation can be expressed as product of two factors. So,
[tex]\begin{gathered} (x-6)(x-2)=0 \\ x\cdot x-6\cdot x-2\cdot x-6\cdot(-2)=0 \\ x^2-6x-2x+12=0 \\ x^2-8x+12=0 \end{gathered}[/tex]Since leading coefficient is 5. So multiply the quadratic equation by 5.
[tex]\begin{gathered} 5(x^2-8x+12)=5\cdot0 \\ 5x^2-40x+60=0 \end{gathered}[/tex]So answer is,
[tex]5x^2-40x+60=0[/tex]