1. 1₁ =2, 12=-2 find the quadratic equation in x with integral coefficients that satisfy the given conditions
Answer (1)
Answer:To find the quadratic equation with integral coefficients satisfying the given conditions:1. 1₁ = 2 (root 1)2. 12 = -2 (root 2)We can use the fact that if p and q are roots of a quadratic equation, then the equation can be written as:(x - p)(x - q) = 0Substituting the given roots:(x - 1)(x + 2) = 0Expanding and simplifying:x² + x - 2 = 0So, the quadratic equation with integral coefficients satisfying the given conditions is:x² + x - 2 = 0Alternatively, we can use the quadratic formula:x = (-b ± √(b² - 4ac)) / 2aHere, a = 1, b = 1, and c = -2 (from x² + x - 2 = 0).
