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In $15-23 :$ a. Find the value of the discriminant and determine if the roots of the quadratic equation are $(1)$ rational and unequal, $(2)$ rational and equal, $(3)$ irrational and unequal, or $(4)$ not real numbers. b. Use any method to find the real roots of the equation if they exist. $$2 x^{2}-8=0$$

(a) Discriminant $=(-8)^{2}-4(2)(0)=64$The discriminant is a perfect square number so the roots of the equation are: (1) rational and unequal(b) The roots are $x=0,4$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 3

The Discriminant

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Oregon State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

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for this equation, we're going to try and find out more about it by taking the disc imminent. This permanent is B squared minus for a C. Is that part of the quadratic formula pratfalls underneath the square and knowing what the value of this is can tell us whether or not the roots are really repeated or uh, like imaginary. So let's just calculated right now. So be is the coefficient on the X term. So since there's no cowfish in there, we do zero over its and zero squared to zero minus four times two times eight would be equal to minus 64. And there's money. 64 is less than zero. We know that there's two imaginary roots actually, actually miscalculated that it's minus eight. So B plus 64 which is great evidence here. So there's two real roots. So since there's two real roots, then using that information, we're able to say we're able to do, uh, at least take the square root of the discrimination to figure out whether they're rational. Rio roots since 64 is a perfect square, it becomes out to eight. So when we closer minus it, we're going to get rational numbers. So there's two riel rational, unequal, rich. So if I was to solve this, I would probably just move the eight to the other side and then sold for X squared. So I get X squared is equal to four. And if I took the square root of four, you get two answers. You get minus two and two, and that makes sense according to what we calculated about the discriminate.

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