A quadratic equation given roots is solved by using the relation
[tex] {x}^{2} - (sum \: of \: roots)x + product \: of \: roots[/tex]
from the question,
sum of the root will be
[tex] \frac{3}{4} + ( - 4) = \frac{3}{4} - 4[/tex]
[tex] = \frac{3 - 16}{4} [/tex]
[tex] = \frac{ - 13}{4} [/tex]
and also, product of the roots will
be
[tex] \frac{3}{4} \times ( - 4) = - 3[/tex]
now substituting the sum of roots and product of roots into the equation
[tex] {x}^{2} - ( - \frac{13}{4} )x - 3[/tex]
[tex] = {x}^{2} + \frac{13}{4} x - 3[/tex]
as the quadratic equation for the root 3/4 and -4
