Solve 4-2x+6x^2

$$4-2x+6 { x }^{ 2 }$$

Factor

$$2\left(3x^{2}-x+2\right)$$

Solution Steps

Factor out 2. Polynomial 2-x+3x^{2} is not factored since it does not have any rational roots.

$$2\left(2-x+3x^{2}\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 6\times 4}}{2\times 6}$$

Square -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 6\times 4}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-\left(-2\right)±\sqrt{4-24\times 4}}{2\times 6}$$

Multiply -24 times 4.

$$x=\frac{-\left(-2\right)±\sqrt{4-96}}{2\times 6}$$

Add 4 to -96.

$$x=\frac{-\left(-2\right)±\sqrt{-92}}{2\times 6}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

$$6x^{2}-2x+4$$

Evaluate

$$6x^{2}-2x+4$$