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For the following, find the discriminant, b2 4ac, and then determine whether one real-number solution, two different real-number solutions Or twO different imaginar...

Question

For the following, find the discriminant, b2 4ac, and then determine whether one real-number solution, two different real-number solutions Or twO different imaginary number solutions exist:Sx? = 8x + 6What is the discriminant;4ac?184 | (Simplify your answer:)What is the nature of the solution(s)?There are two different imaginary-number solutions: There one real-number solution_There are two different real-number solutions_

For the following, find the discriminant, b2 4ac, and then determine whether one real-number solution, two different real-number solutions Or twO different imaginary number solutions exist: Sx? = 8x + 6 What is the discriminant; 4ac? 184 | (Simplify your answer:) What is the nature of the solution(s)? There are two different imaginary-number solutions: There one real-number solution_ There are two different real-number solutions_



Answers

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.
$$2 x^{2}-6 x+7=0$$

In this problem, we have three x squared plus Pyrex dynasty. And we need to use the discriminatory to tell us how many solutions that's quadratic has. Now remember the discriminative B squared minus four e c. So we wait list. So he squared is five squared, which is 25 minus four times a, which is three I'm c, which is negative eight. Now, if we multiply these out, we get negative eight times three, which is negative 24 times negative, or which is comes out positive 96 and now, without even having to add 25 96 together we see it's most definitely above Zira. So that means that this function has to real solutions.

So we're gonna look at the equation X squared plus six X plus eight people zero and many's the discriminative to calculate how many solutions we have. So the discriminative B squared minus four a. C is the coefficient of X squared, which is one B is coefficient of X, which is six and C is the constant, which is eight. So let's put that into the discriminative, and so it wouldn't get so sick squared minus four times one times eight. And then if we put that into our calculator six squared minus four times one times eight we will get for and when the discriminative is greater than zero. So it's a positive number we get to riel solutions.

According to the question, we have been given a Kordic equation except square last 66 plus eight equals zero. Now this coordinated equation is already here in present in the standard from We also know that the standard form and according to recent can be represented by X descriptors. We explicit. So if you compare aboard the equations, then we will have equals one v equal. Six on a seek was eight now the distant off Accordingly, depression, which is represented in standard form, can be given by the form Love the square minus four a c. Now, since we already have the values off A B and C so we can subsequently in this given formula and we will have the square that six services cut six minus four, multiplied by one, multiplied by eight. So eight mullah crack before is tell you to the minds of 30 do for the equals 36 months 32 with physical sport now say the equals four on four can be written as to list real power to that is we can we can what I d in the form of a square or we can write. We can convert the in the form of a square. So the roots of the given card ejaculation will be really production in nature and a number of fruits number off roots will be equals food. So we will have to really solution to really rational solutions, obviously Vanguard calculation.

So for this problem, we're supposed to find the discriminative, decide how maney solutions there are. So to find the discriminate, we need to look. Our quadratic formula X squared equals negative B plus or minus the square root of B squared minus four a c all divided by two A. We're going to use this part of the equation. I'm gonna go ahead and label my A might be here in my seat, so we're gonna say B squared. So negative one square minus four six. And that too gonna give me one minus 24 times neck to give small a negative 48. Or you could say one plus 48 which is 40 nine now when b squared minus four A. C is greater than zero. That means we have to rial solutions. It is equal to zero. We have one really solution. Nivea Tous les Fun. You have no rial solutions 40 49 It's definitely grated. Zero The trains We have to really solutions


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