SOLUTION: Could you help me state the degree, number of complex roots, and leading coefficient of 3x^4-x^3+5x^2+12x-7=0

Question 392447: Could you help me state the degree, number of complex roots, and leading coefficient of 3x^4-x^3+5x^2+12x-7=0
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Degree is 4 since the highest power of x that has a nonzero coefficient is 4.

There's a very important theorem called the Fundamental theorem of algebra (in which the proof is quite complex) that says that any single variable polynomial of degree n has n complex roots (including multiple roots). Since the degree is 4, the polynomial must have four complex roots. Note that real numbers are still considered complex, by definition.

The leading coefficient is 3 (coefficient of the highest degree term).
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