12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.)

Respuesta :

In general, a quadratic equation can be written in terms of its solutions:

[tex]y=(x-a)(x-b).[/tex]

Now, notice that:

[tex]x+\frac{1}{2}=0\text{ }[/tex]

when x= -1/2, and it is equivalent to:

[tex]2x+1=0.[/tex]

Therefore, you can write the quadratic equation as:

[tex]y=(2x+1)(x-4).[/tex]

Computing the above multiplication, you get:

[tex]y=2x^2-8x+x-4.[/tex]

Simplifying the above equation you get:

[tex]y=2x^2-7x-4.[/tex]

Answer:

[tex]y=2x^{2}-7x-4[/tex]