Question 199414
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I don't know what a 'discriminate' means with respect to a quadratic polynomial.  And you do not have an equation since there is no equals sign.  So I can't precisely answer the question you posed.


However, if you meant:

"I need to calculate the <i>discriminant</i>, determine the number of solutions, and classify the solutions for the equation:  sqrt(2)x^2-4x-7*sqrt(2)<b>=</b>0"


Then I can help.


Given a quadratic equation in standard form, namely:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ax^2 + bx + c = 0]


You can calculate the discriminant, *[tex \Large \Delta], by substituting the given coefficients into:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta = b^2 - 4ac]


Then you can classify the roots of the equation thus:


*[tex \LARGE \Delta > 0 \ \ \Rightarrow\ \] Two real and unequal roots.


*[tex \LARGE \Delta = 0 \ \ \Rightarrow\ \] One real root with a multiplicity of two.  That is to say that the trinomial is a perfect square and has two identical factors.


*[tex \LARGE \Delta < 0 \ \ \Rightarrow\ \] A conjugate pair of complex roots of the form *[tex \LARGE a \pm bi] where *[tex \LARGE i] is the imaginary number defined by *[tex \LARGE i^2 = -1]


For your problem: *[tex \Large a = \sqrt{2}], *[tex \Large b = -4], and *[tex \Large c = -7\sqrt{2}], so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta = (-4)^2 - 4(\sqrt{2})(-7\sqrt{2})]


You can do your own arithmetic and then evaluate according to the criteria listed.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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