x^(2)+(1-a)x+a^(2)-(6)/(4)a-(3)/(4)=0

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Identify Quadratic Equation: We are given the quadratic equation x^2 + (1-a)x + a^2 - (6/4)a - (3/4) = 0. To find the roots, we need to solve for x. The general form of a quadratic equation is ax^2 + bx + c = 0, and the roots can be found using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a). In our case, a = 1, b = (1-a), and c = a^2 - (6/4)a - (3/4).Simplify Constant Term: First, let's simplify the constant term c by combining like terms: a^2 - (6/4)a - (3/4). We can write (6/4)a as (3/2)a to make it easier to combine with (3/4). c = a^2 - (3/2)a - (3/4)Calculate Discriminant: Now, let's calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (1-a)^2 - 4(1)(a^2 - (3/2)a - (3/4))Expand and Simplify: We expand (1-a)^2 and simplify the expression: Discriminant = (1 - 2a + a^2) - 4(a^2 - (3/2)a - (3/4))Combine Like Terms: Distribute the -4 across the terms in the parentheses: Discriminant = 1 - 2a + a^2 - 4a^2 + 6a + 3Use Quadratic Formula: Combine like terms to simplify the discriminant: Discriminant = 1 - 2a + a^2 - 4a^2 + 6a + 3 Discriminant = -3a^2 + 4a + 4Formula for Roots: Now we can use the quadratic formula to find the roots: x = [-(1-a) ± sqrt(-3a^2 + 4a + 4)] / (2*1) x = [-(1-a) ± sqrt(-3a^2 + 4a + 4)] / 2We have found the formula for the roots of the quadratic equation in terms of a. The roots will depend on the value of a, and we can use this formula to find specific roots for any given value of a.

$x^{2}+(1-a) x+a^{2}-\frac{6}{4} a-\frac{3}{4}=0$

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$x^{2}+(1-a) x+a^{2}-\frac{6}{4} a-\frac{3}{4}=0$