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
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-> 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
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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).
