A. what is the sum of the squares of the roots of $x^2 - 5x - 4 = 0$? b. one root of $x^2 + 12x + k = 0$ is twice the other root. find $k.$ c. what is the sum of the roots of the quadratic $4x^2 - 4x - 4$? d. jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ he assumes that it will factor in the form \[ax^2 + bx + c = (ax + b)(cx + d),\]where $a,$ $b,$ $c,$ and $d$ are integers. if $a = 4,$ and jimmy wants to find the value of $a,$ what are the possible values he should check, in order to find $a$? e. brandy is trying to factor the quadratic $3x^2 - x - 10.$ she starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + b)(3x + d),\]for some integers $b$ and $d.$ after some work, brandy successfully factors the quadratic. find the ordered pair $(b, d).$