But for finding the nature of the roots, we don't actually need to solve the equation. two real and equal roots (it means only one real root)įor example, in the above example, the roots of the quadratic equation x 2 - 7x + 10 = 0 are x = 2 and x = 5, where both 2 and 5 are two different real numbers, and so we can say that the equation has two real and different roots.The nature of the roots of a quadratic equation talks about "how many roots the equation has?" and "what type of roots the equation has?". So the best methods that always work for finding the roots are the quadratic root formula and completing the square methods. Note that the factoring method works only when the quadratic equation is factorable and we cannot find the complex roots of the quadratic equation using the graphing method. We can observe that the roots of the quadratic equation x 2 - 7x + 10 = 0 are x = 2 and x = 5 in each of the methods. Therefore, the roots of the quadratic equation are x = 2 and x = 5. Solution: To solve this, we just need to graph f(x) = x 2 - 7x + 10 and identify the x-intercepts. Identify the x-intercepts which are nothing but the roots of the quadratic equation.Įxample: Find the roots of the quadratic equation x 2 - 7x + 10 = 0 by graphing.Graph the left side part (the quadratic function) either manually or using the graphing display calculator (GDC).X = 5, x = 2 Finding Roots of Quadratic Equation by Graphing Now, taking the square root on both sides: Solve by taking square root on both sides.Įxample: Find the quadratic roots of x 2 - 7x + 10 = 0 by completing square.īy completing the square, we get (x - (7/2) ) 2 = 9/4. Finding Roots of Quadratic Equation by Completing Square
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