Question

find the quadratic equation if its solutions are 1.5 and -.25, and the equation coefficients are not decimals.

Answer 1

If a quadratic equation has solutions $x_1$ and $x_2$, then we can write it as

$(x-x_1)(x-x_2)$

So, in your case, we have (let me write 1.5 as 3/2 and -0.25 as -1/4)

$\left(x-\dfrac{3}{2}\right)\left(x+\dfrac{1}{4}\right) = x^2-\dfrac{5}{4}x-\dfrac{3}{8}$

If we don't want decimal coefficient, we can multiply the whole expression by 8:

$8x^2-10x-3$