Answers to Matched Exercises on Quadratic Equations (1)
Answers to Matched Exercises in the tutorial of Solve Quadratic Equations Using Discriminants (1)
Matched Exercise 1Find all solutions to the quadratic equation given below.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 2Find all solutions to the quadratic equation.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 3Find 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 LinksSolve Equations, Systems of Equations and Inequalities. |