The quadratic equation will be[tex]x^2 -11x +28 =0[/tex]
Step-by-step explanation:
To frame the quadratic equation using the solutions as 4 and 7, we can go in the reverse order of finding the solution.
- Then solutions can be written as [tex](x-4)[/tex] and [tex](x-7)[/tex]
- Now, taking the product of the two terms and equating to zero
[tex](x-4)(x-7)=0[/tex]
- On multiplication, we obtain,
[tex]x^2-7x-4x+28 = 0[/tex]
[tex]x^2 -11x +28 =0[/tex]
- Hence, the desired quadratic equation is [tex]x^2 -11x +28 =0[/tex]