Question

Can you help and explain Apply the zero peoduct theorem to solve for value of x
`x { = 9}^(2)`
`27x {}^(2) = 9x`

Answer 1

We want to solve

`27x^2=9x\text{ using zero product thorem}`

The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

For the question,

`\begin{gathered} 27x^2=9x \\ \text{Divide both sides by }9 \\ 3x^2=x \\ \text{Subtract x from both sides} \\ 3x^2-x=0 \\ \text{Factorize} \\ x(3x-1)=0 \\ \text{Applying the zero theroem, we have} \\ x=0\text{ or 3x-1=0} \\ x=0\text{ or 3x = 1} \\ x=0\text{ or x = }(1)/(3) \end{gathered}`

The answer is x = 0 and x = 1/3