Find the Roots (Zeros) f(x)=4x^2+2x+6

$f (x) = 4 x^{2} + 2 x + 6$

Step 1

Set $4 x^{2} + 2 x + 6$ equal to $0$ .

$4 x^{2} + 2 x + 6 = 0$

Step 2

Solve for $x$ .

Factor $2$ out of $4 x^{2} + 2 x + 6$ .

Factor $2$ out of $4 x^{2}$ .

$2 (2 x^{2}) + 2 x + 6 = 0$

Factor $2$ out of $2 x$ .

$2 (2 x^{2}) + 2 (x) + 6 = 0$

Factor $2$ out of $6$ .

$2 (2 x^{2}) + 2 x + 2 \cdot 3 = 0$

Factor $2$ out of $2 (2 x^{2}) + 2 x$ .

$2 (2 x^{2} + x) + 2 \cdot 3 = 0$

Factor $2$ out of $2 (2 x^{2} + x) + 2 \cdot 3$ .

$2 (2 x^{2} + x + 3) = 0$

Divide each term in $2 (2 x^{2} + x + 3) = 0$ by $2$ and simplify.

Divide each term in $2 (2 x^{2} + x + 3) = 0$ by $2$ .

$\frac{2 (2 x^{2} + x + 3)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (2 x^{2} + x + 3)}{2} = \frac{0}{2}$

Divide $2 x^{2} + x + 3$ by $1$ .

$2 x^{2} + x + 3 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$2 x^{2} + x + 3 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 2$ , $b = 1$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot 3}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 1 \pm \sqrt{1 - 8 \cdot 3}}{2 \cdot 2}$

Multiply $- 8$ by $3$ .

$x = \frac{- 1 \pm \sqrt{1 - 24}}{2 \cdot 2}$

Subtract $24$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 23}}{2 \cdot 2}$

Rewrite $- 23$ as $- 1 (23)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 23}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (23)}$ as $\sqrt{- 1} \cdot \sqrt{23}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{23}}{2 \cdot 2}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{23}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 1 \pm i \sqrt{23}}{4}$

The final answer is the combination of both solutions.

$x = - \frac{1 - i \sqrt{23}}{4}, - \frac{1 + i \sqrt{23}}{4}$

$x = \frac{- 1 \pm i \sqrt{23}}{4}$

Step 3

Find the Roots (Zeros) f(x)=4x^2+2x+6

Related Questions

Support LCMGCF.com by disabling your adblocker.