DIS QUES #1 Week 7

DIS QUES #1 Week 7 - and x = -b. The quadratic equation...

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To decide whether a quadratic equation has one, two or no solutions, we calculate its determinant. We will be able to distinguish solutions by looking at the discriminate D = b^2 - 4c. We will be able to distinguish solutions by looking at the discriminate D = b^2 - 4c. Keep in mind that when D > 0, Then that means that P(x) has two distinct REAL roots and therefore two solutions. However, when D < 0, P(x) has no REAL roots and therefore no solution can be defined and if D = 0, then P(x) would have 2 coincident REAL roots but only one solution. For a quadratic equation of the form: ax 2 + bx + c = f(x), the determinant is given by b 2 – 4*a*c. Finding a quadratic equation by its solution can be easily done if one was given the roots of x = a
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Unformatted text preview: and x = -b. The quadratic equation would be (x-a)(x+b) = 0. Its possible to have different quadratic equations with the same solutions. This is possible, if we take the example here as evidence; the equations f(x) = 4x 2 and g(x) = -4x 2 share the same solution, x=0, although they are different equations. For example, this quadratic equation of X, with X remaining constant; (x-a)(x+b) = 0. If being asked to multiply by the constant, we would find that it does not change the roots. Also, if we have the solutions of the quadratic equation and those solutions are x 1 and x 2 , then the equation is obtained by expanding the product....
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This note was uploaded on 01/04/2011 for the course MAT 117 taught by Professor Al-kofahi during the Spring '09 term at University of Phoenix.

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