![]() ![]() Quadratic equations that have negative discriminant values, their roots are represented by complex numbers.Generally, we solve the quadratic equations through factorization, however, we use the quadratic formula when it cannot be solved by factorization.Here are a few tips and tricks to solve quadratic equations in a simpler and easier manner. Tips and Tricks for Solving Quadratic Equations Graphical Method to Solve Quadratic Equations We can also obtain the points algebraically by equalizing the y value to 0 in the function y = ax 2 + bx + c and solving for x. The point(s) where the graph intersects the x-axis is the solution of the quadratic equation. With the setting, y = – 2, –1, and 0, we getīy solving and substituting values for x, we can obtain values of y and obtain numerous points which can be plotted on the coordinate axis to obtain a parabola-shaped graph for the quadratic equation. The present age of his daughter is represented as = yīased on the question, (x – 7) = 7 (y – 7 )Īccording to the question, (x + 3) = 3 (y + 3) Solution: Let the present age of Aftab = x Additionally, three years from now, I will be three times as old as you will be.” This represents this example algebraically and graphically. The graphical method can be understood with the help of the given example:Įxample: Aftab tells his daughter, “seven years ago, I was seven times as old as you were then. The '+' and '-' sign gives both the roots of the quadratic equation.Ĭompleting the square method is quite detailed and lengthy and is generally avoided. On simplifying the equation further and taking the square root, the two roots are x = (-b + √(b 2- 4ac))/2a. Next, express the left-hand side as a perfect square, by adding a new term (b/2a) 2 on both sides: In order to determine the roots of the quadratic equation ax 2 + bx + c = 0, we need to first simplify it Read More: Complex Numbers & Quadratic Equations Important Questions Completing the Square MethodĬompleting the square method involves algebraically squaring and simplifying the quadratic equation to obtain the required roots. Therefore, 1 and 3/2 are the roots of the given equation. A quadratic equation will become an identity (a, b, c = zero) if the equation is solved by using more than two numbers, that is, having extra than two roots either real or complicated.Įxample: Consider a quadratic equation 2x 2−5x+ 3= 0.If a ![]() D zero, minimal value = 4ac – b 2/4a at x = -b/2a. ![]()
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