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Sowve tha equaton; pesslble 42+Font FamilyWhat are all the rots 0t%' 46r" 36t?Font FamilyAA -5 4f5 2ndare roots of & polynomial with Integer coefficl...

Question

Sowve tha equaton; pesslble 42+Font FamilyWhat are all the rots 0t%' 46r" 36t?Font FamilyAA -5 4f5 2ndare roots of & polynomial with Integer coefficlents, what must be aother root?

Sowve tha equaton; pesslble 42+ Font Family What are all the rots 0t%' 46r" 36t? Font Family AA - 5 4f5 2nd are roots of & polynomial with Integer coefficlents, what must be aother root?



Answers

a. Using real and imaginary as types of roots, list all possible combinations of
root type for a fourth-deegree polynomial equation.
b. Repeat to process for a fifth-degree polynomial equation.
c. Make a Conjecture Make a conjecture about the number of real roots of an
odd-degree polynomial equation.

The given doors as minus outta on DDE For out I will write the polynomial using these roots as X plus our daughter in tow X minus for outer. That is equal to Gino because gives it's a Squire. Bless ex outta minus four x I would, uh, minus for our Squire is equal to zero and is equal to x Esquire plus X times off outta minus four. Out plus four is equal. Fujito, this is off the farm. It's a Squire less x times off on surplus Vita Plus on Bobby dies equal Hagino, there have been cases of the farm, which is our Squire. Plus, next time So far, Peter Plus alphabetize your Jiro and we have been all problems beat our Is he gonna do our time? Minus four out on Alpha Beta that is equal to four and started Schneider's rules, uh, are turned minus for iota. These are the to lose and this is the answer

Here we are given a quarter of the equation. That is model is y squared minus more. Do I -2 is equal to zero. So we need to find the rule of this equation. So let us this can be factories as more or less of y squared minus for more white Plus three. Mode, Y -12 Is equal to zero. That is more lots of Windows Models of Y -4 Plus three. In the models of Why AM -4 Is the Old zero. That is models of y minus for India Models of by Plus three, He goes to zero. Therefore, models of why can take values four or -3. And since it is a model is function will not take -3. They have a models of Y is equal to four. That is why can take values Plus or -4. These are the rules of discriminate question.

If we have these three solutions to a polynomial with riel coefficients, we're gonna have to additional solutions because imaginary solutions must come in pairs. So we have negative three I we're also going to have to have positive three I and a conjugal pair. If we have five minus three, I we're also gonna have to have lost three I. The same requirement is not true for real numbers, so we do not need to have a negative three. A swell, but conjugated pairs means that we must have the positive and negative of the imaginary number. So our answer would be choice too and choice through which gives us letter choice H.

And this problem will be finding 1/3 degree call normal equation with negative five and one minds. There are only two, uh, roots given in this problem. But we also know that one plus I is also a group because it is the congregate of one mind. So now you don't find the factors off the cooling milieu, which are X negative X minus Negative five X minus one minus I and X minus one plus I. So now, uh, to find the pollen? No, no, we just need a multiply all these three factors and go everything. So x plus five x minus one plus I x minus one minus phi. So for days to when you multiply these, you can use the difference of square. So these are specters. And so when you multiply the cell, you could x squared minus two x course one close one And then you just want to quit everything. And here is your answer


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