Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots. x6+15x5+7x4−18x3−5x2+17x+6____
Q. Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots. x6+15x5+7x4−18x3−5x2+17x+6____
Identify highest power of x: Look at the polynomial: x6+15x5+7x4−18x3−5x2+17x+6. Identify the highest power of x, which is 6.
Apply Fundamental Theorem of Algebra: According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex roots, counting multiplicity.So, this polynomial has 6 complex roots.