Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. $$ f(x)=-2+x^{4}-3 x^{7}+6 x^{6} $$ Degree $$ = $$ Leading Coefficient $$ = $$ Maximum number of real zeros $$ =\square $$

Question

UpStudy AI · Accepted Answer

1. Identify the highest exponent in the polynomial  
   The polynomial is  
   $$
   f(x)=-2+x^{4}-3x^{7}+6x^{6}
   $$  
   The term $$ -3x^7 $$ has the highest exponent $$ 7 $$.

2. Determine the degree  
   The degree of the polynomial is the highest exponent, so  
   $$
   \text{Degree} = 7
   $$

3. Find the leading coefficient  
   The leading coefficient is the coefficient of the term with the highest degree. Here, it is the coefficient of $$ x^7 $$, which is  
   $$
   \text{Leading Coefficient} = -3
   $$

4. Calculate the maximum number of real zeros  
   A polynomial of degree $$ 7 $$ can have at most $$ 7 $$ real zeros (by the Fundamental Theorem of Algebra, it has 7 zeros counting multiplicity, and if all are real, the maximum number is 7).  
   $$
   \text{Maximum number of real zeros} = 7
   $$
Degree = 7 Leading Coefficient = -3 Maximum number of real zeros = 7

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. \( f(x)=-2+x^{4}-3 x^{7}+6 x^{6} \) Degree \( = \) Leading Coefficient \( = \) Maximum number of real zeros \( =\square \)

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions