Whats the right answer
How many real zeroes does y = ( x + 8 )3 + 9 have?
(1 point)
Responses
1
1
2
2
3
3
0
The right answer is: 1
To determine how many real zeroes the equation y = (x + 8)^3 + 9 has, we need to understand what real zeroes indicate in the context of a polynomial function.
Real zeroes of a polynomial function are the values of x that make the function equal to zero. In this case, the polynomial function is y = (x + 8)^3 + 9.
To find the real zeroes of a polynomial function, we set the function equal to zero and solve for x.
Setting (x + 8)^3 + 9 = 0, we can start by subtracting 9 from both sides:
(x + 8)^3 = -9
Next, we take the cube root of both sides to isolate x + 8:
∛[(x + 8)^3] = ∛(-9)
x + 8 = -∛9
Finally, we subtract 8 from both sides to solve for x:
x = -∛9 - 8
By solving the equation, we find a single real zero for the function y = (x + 8)^3 + 9. Therefore, the correct answer is 1.
To find the number of real zeroes for the equation y = (x + 8)^3 + 9, we can analyze the power and sign changes.
Step 1: Identify the power of the polynomial. In this case, the power of the polynomial is 3.
Step 2: Determine the sign changes. If the sign of the coefficients changes across the polynomial, then there will be a corresponding number of real zeroes. In this equation, the sign does not change because the exponent is an odd number (3). Therefore, there are no sign changes.
Step 3: Determine the number of real zeroes. Since there are no sign changes, there are no real zeroes.
So, the answer is 0.