Find the Roots (Zeros) f(x)=x^3-14x^2+49x

$f (x) = x^{3} - 14 x^{2} + 49 x$

Set $x^{3} - 14 x^{2} + 49 x$ equal to $0$ .

$x^{3} - 14 x^{2} + 49 x = 0$

Solve for $x$ .

Tap for more steps…

Factor the left side of the equation.

Tap for more steps…

Factor $x$ out of $x^{3} - 14 x^{2} + 49 x$ .

Tap for more steps…

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} - 14 x^{2} + 49 x = 0$

Factor $x$ out of $- 14 x^{2}$ .

$x \cdot x^{2} + x (- 14 x) + 49 x = 0$

Factor $x$ out of $49 x$ .

$x \cdot x^{2} + x (- 14 x) + x \cdot 49 = 0$

Factor $x$ out of $x \cdot x^{2} + x (- 14 x)$ .

$x (x^{2} - 14 x) + x \cdot 49 = 0$

Factor $x$ out of $x (x^{2} - 14 x) + x \cdot 49$ .

$x (x^{2} - 14 x + 49) = 0$

Factor using the perfect square rule.

Tap for more steps…

Rewrite $49$ as $7^{2}$ .

$x (x^{2} - 14 x + 7^{2}) = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot - 7$

Simplify.

$2 a b = - 14 x$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = - 7$ .

$x {(x - 7)}^{2} = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

${(x - 7)}^{2} = 0$

Set the first factor equal to $0$ .

$x = 0$

Set the next factor equal to $0$ and solve.

Tap for more steps…

Set the next factor equal to $0$ .

${(x - 7)}^{2} = 0$

Set the $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make $x {(x - 7)}^{2} = 0$ true.

$x = 0, 7$

Find the Roots (Zeros) f(x)=x^3-14x^2+49x

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store