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Equations of 2nd degree or more. Question related to quadrants.?
Just a few minutes back Mathmom answered that a cubic equation will start in Q3 and end in Q1 if a > 0. Can someone tell me what is the relation between the coefficients and the quadrants. Equation to be considered of the general form ax^n + bx^(n-1) ...... = 0. Don't need details, hints will do. Thanks.
1 Answer
- Rita the dogLv 78 years agoFavorite Answer
If the leading coefficient of a polynomial (i.e. coefficient of highest power of x) is positive and the polynomial has odd degree, then for x sufficiently small (i.e. negative far enough) the polynomial will be negative (i.e. in QIII), and for x sufficiently large x (i.e. positive far enough) the polynomial will be positive (i.e. in QI).
The highest power of x always dominates for |x| large (i.e. "large negative" or large positive).
So, if the polynomial is of even degree and the leading coefficient is positive, it is eventually positive, so to the left far enough it will be in QII and to the right far enough the graph will be in QI.
(The above edited slightly to fix omission).
