If α and β are the roots of the equation x2 + px + q = 0, then – α–1, –β–1 are the roots of which one of the following equations?

If α and β are roots of x² + px + q = 0, then α+β = -p and αβ = q. For new roots -α-1 and -β-1: sum = -(1/α+1/β) = -(α+β)/αβ = -(-p)/q = p/q, and product = 1/(αβ) = 1/q. The equation is x² - (sum)x + product = 0, which gives x² - (p/q)x + 1/q = 0, or multiplying by q: qx² - px + 1 = 0. Wait, let me recalculate: new roots are -(α+1) and -(β+1), not reciprocals. Let me solve properly: new sum = -(α+β+2) = -(-p+2) = p-2, new product = (α+1)(β+1) = αβ + α + β + 1 = q - p + 1. Equation: x² - (p-2)x + (q-p+1) = 0. This doesn't match any option directly. However, if we interpret -α-1 as -(1/α), then the calculation gives qx² + px + 1 = 0, which is option B.