Question

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.)

Answer 1

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

`y=(x-a)(x-b).`

Now, notice that:

`x+(1)/(2)=0\text{ }`

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

`2x+1=0.`

Therefore, you can write the quadratic equation as:

`y=(2x+1)(x-4).`

Computing the above multiplication, you get:

`y=2x^2-8x+x-4.`

Simplifying the above equation you get:

`y=2x^2-7x-4.`

Answer:

`y=2x^(2)-7x-4`