True or False
2006-10-22 03:49:01 · 4 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics
i would say true
2006-10-22 03:54:10 · answer #1 · answered by cheesy 2 · 0⤊ 1⤋
Yes....even if P(x) has a degree 2, even then it would be having a minimum(at the vertex of parabola it forms).The x co-ordinate gives the value at which it would be having its minimum value.
In other case, if P(x) has an even degree greater than 2, the condition would stand valid that it has at least one minimum(local as well as global). The reason behind the fact being the derivative of P(x) would be a polynomial of odd degree. And a polynomial having odd degree greater than or equal to 3 has at least one real root implying a point of extremum. So as per first derivative test, derivative of P(x) would be positive on both sides of points of extremum. This implies this extremum is nothing but the minimum of P(x).
Hope you are satisfied by this answer.take care, bye.
2006-10-22 04:03:15 · answer #2 · answered by Supriya Tyagi 2 · 1⤊ 0⤋
Yes, as has been said, but they will all be complex or imaginary. Also, the trivial case where the order is zero will have no minimum or maximum.
2006-10-22 08:08:36 · answer #3 · answered by aristotle2600 3 · 0⤊ 0⤋
This is a true statement. But it also means that P(x) will never have real roots, they will always be complex numbers that come in conjugate pairs.
2006-10-22 04:16:21 · answer #4 · answered by ironduke8159 7 · 1⤊ 0⤋