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MAT117Week8ExerciseConceptCheck

MAT117Week8ExerciseConceptCheck - roots and one is the...

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MAT/117 Week 8 Exercise: Concept Check Post a response to the following: If you are looking at a graph of a quadratic equation, how do you determine where the solutions are? The solution(s) are located where the graph crosses the x axis. At the x axis, x = 0, so that makes the crossing(s) the solution(s) of the equation ax^2 + bx + c = 0   The solutions will be on the horizontal x axis of the graph (look for the x-intercepts). When the graph crosses the x-axis at two distinct points, (the equation has two distinct, real roots). When the graph has a single point where it touches the x-axis, (the equation has a repeated, real root). Or if the graph never touches the x-axis, (the equation has a pair of complex
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Unformatted text preview: roots and one is the conjugate of the other. The basis that confirms this is called the discriminant, and this is the term inside the square root of the quadratic formula for ax² + bx + c = 0: b² - 4ac. Now if the discriminant is positive, the equation has two real, distinct roots. If the discriminant is zero, the equation has two repeated roots. If it is negative, the equation has two complex conjugate roots. The (real) solutions are whenever the graph crosses the x-axis at y=0 This can also be determined mathematically by factoring: x^2+2x+1 (x+1)(x+1) The graph would cross at (0,-1)...
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