+1622 We have a quadratic, and since the first step is to find the roots, we can apply the quadratic formula: \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\), where \(a\) is the coefficient of \(x^2\), \(b\) is the coefficient of \(x\), and \(c\) is the constant.
Now to plug in the values.
\(x = {-1{+\over}\sqrt{13}\over2}\)
The plus operation and the minus operation are the roots p and q, respectively.
Now I used a calculator, and \(4p^2\) approximates to 6.7889.
\(q^3\) approximates to -12.2111.
Since we are subtracting \(q^3\) from \(4p^2 \), that is 6.7889 - (-12.2111) = 19.
Thus, \(4p^2 - q^3 = 19\).
