What are the zeroes of the polynomial equation, 𝑦 = 𝑥3 + 3𝑥2
I will assume you mean:
y = x^3 + 3x^2 , notice how we show exponents here
x^3 + 3x^2 = 0
x^2(x + 3) = 0
finish it up
To find the zeroes of a polynomial equation, you need to solve for the values of x when y equals zero. In this case, we are given the polynomial equation 𝑦 = 𝑥^3 + 3𝑥^2.
Setting 𝑦 equal to zero, we have:
0 = 𝑥^3 + 3𝑥^2
To solve this equation, we can factor out a common factor of 𝑥^2:
0 = 𝑥^2(𝑥 + 3)
Now we have two possible cases to consider:
Case 1: 𝑥^2 = 0
This means that 𝑥 = 0 since any number squared is equal to zero only when the number itself is zero.
Case 2: 𝑥 + 3 = 0
Subtracting 3 from both sides of the equation, we get 𝑥 = -3.
Therefore, the zeroes of the polynomial equation 𝑦 = 𝑥^3 + 3𝑥^2 are 𝑥 = 0 and 𝑥 = -3.