Answers to Matched Exercises on Quadratic Equations (1)
Answers to Matched Exercises in the tutorial of Solve Quadratic Equations Using Discriminants (1)
Matched Exercise 1: Find all solutions to the quadratic equation given below.
x ^{2} - 3 x + 2 = 0 Answer to Matched Exercise 1:We use the quadratic formulas. The disriminant D = b^{ 2} - 4 a c = (-3)^{ 2} - 4 (1) (2) = 1. Since the discriminant is positive, the above equation has two real solutions x_{1} = (-b + √D) / (2 a) = (3 + 1) / 2 = 2 x_{2} = (- b - √D) / (2 a) = (3 - 1) / 2 = 1
Matched Exercise 2.Find all solutions to the quadratic equation.x ^{2}/2 = - 8 - 4x Answer to Matched Exercise 2:Multiply all terms in the above equation by 2 and write it in standard form. x ^{2} + 8x + 16 = 0 The disriminant D = 0. Since the discriminant is equal to zero, the above equation one real solution. x = - 4
Matched Exercise 3.Find all solutions to the quadratic equation.x ^{2} - 4x + 5 = 0 Answer to Matched Exercise 3:The disriminant D = - 4. Since the discriminant is negative, the above equation has two imaginary solutions. x = 2 + i x = 2 - i where i = √(-1) is the imaginary unit. More References and linksMore references and links on how to Solve Equations, Systems of Equations and Inequalities. |