Questions: Solve for x. x^3 + 6x^2 - 7x = 0 x = [?]

Transcript text: Solve for x . \[ \begin{array}{l} x^{3}+6 x^{2}-7 x=0 \\ x=[?] \end{array} \]

Solution

Solution Steps

Step 1: Factor the Polynomial

We start with the polynomial equation: \[ x^{3} + 6x^{2} - 7x = 0 \] Factoring this polynomial, we obtain: \[ x \left(x - 1\right) \left(x + 7\right) = 0 \]

Step 2: Set Each Factor to Zero

To find the roots, we set each factor equal to zero:

\( x = 0 \)
\( x - 1 = 0 \) which gives \( x = 1 \)
\( x + 7 = 0 \) which gives \( x = -7 \)

Step 3: List the Roots

The roots of the polynomial are: \[ x = -7, \quad x = 0, \quad x = 1 \]

Step 4: Identify the Smallest Root

Among the roots, the smallest value is: \[ \text{Smallest Root} = -7 \]

Final Answer

\(\boxed{-7}\)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >