Please help!! I do not understand any of this!!
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree 3; zeros: 8, -6-i
zeros mean in the numerator you have...
(x-8)*(x+6+i)
that is degree two.
Now real numbers mean the complex cannot be allowed, so one adds the conjugate of the complex, so
y(x)=(x-8)*(x+6+i)*(x+6-i)
i need help i have a polynomial f(x) whose coefficeint are real numbers. Find the remaining zeros of f. Degree 3, zeros -4,-2,-i
I'm here to help! First, let's clarify some concepts. A polynomial is an algebraic expression that consists of variables, coefficients, and exponents. The degree of a polynomial is the highest power of the variable in the expression.
In your case, the polynomial is denoted as f(x), and it has a degree of 3. You are given two zeros: 8 and -6-i. Remember that a zero of a polynomial is a value of x for which f(x) equals zero.
To find the remaining zeros of f(x), we should start by using the given zeros to construct factors of the polynomial. Since the coefficients are real numbers, we know that complex zeros occur in conjugate pairs.
1. Use the zero 8: If 8 is a zero of f(x), then (x - 8) is a factor of the polynomial.
2. Use the zero -6-i: Since the coefficients are real, we know that -6+i is also a zero. Therefore, (x - (-6-i)) = (x + 6 + i) is a factor of the polynomial.
Now, to find the remaining zero, we need to find the remaining factor of the polynomial.
3. Divide the polynomial by the two factors: Divide f(x) by (x - 8) and (x + 6 + i) using polynomial division. The result will be a quadratic polynomial that we can solve to find the remaining zero.
Once we have the remaining factor or the quadratic polynomial, we can solve it using methods like factoring, completing the square, or using the quadratic formula, depending on the nature of the equation.
By following these steps, you should be able to find the remaining zeros of the polynomial f(x). If you have the actual polynomial expression, please share it, and I would be happy to guide you further!