Solve k^2-4(-1/4)(-3)=0

$$k ^ { 2 } - 4 ( - \frac { 1 } { 4 } ) ( - 3 ) = 0$$

Solve for k

$$k=\sqrt{3}\approx 1.732050808$$

$$k=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Multiply 4 and -\frac{1}{4} to get -1.

$$k^{2}-\left(-\left(-3\right)\right)=0$$

Multiply -1 and -3 to get 3.

$$k^{2}-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$k^{2}=3$$

Take the square root of both sides of the equation.

$$k=\sqrt{3} k=-\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply 4 and -\frac{1}{4} to get -1.

$$k^{2}-\left(-\left(-3\right)\right)=0$$

Multiply -1 and -3 to get 3.

$$k^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-3\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-3\right)}}{2}$$

Multiply -4 times -3.

$$k=\frac{0±\sqrt{12}}{2}$$

Take the square root of 12.

$$k=\frac{0±2\sqrt{3}}{2}$$

Now solve the equation k=\frac{0±2\sqrt{3}}{2} when ± is plus.

$$k=\sqrt{3}$$

Now solve the equation k=\frac{0±2\sqrt{3}}{2} when ± is minus.

$$k=-\sqrt{3}$$

The equation is now solved.

$$k=\sqrt{3} k=-\sqrt{3}$$