Find the Discriminant 4k^2+5k+4=-3k

$4 k^{2} + 5 k + 4 = - 3 k$

Step 1

Move all terms to the left side of the equation and simplify.

Add $3 k$ to both sides of the equation.

$4 k^{2} + 5 k + 4 + 3 k = 0$

Add $5 k$ and $3 k$ .

$4 k^{2} + 8 k + 4 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

$8^{2} - 4 (4 \cdot 4)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $8$ to the power of $2$ .

$64 - 4 (4 \cdot 4)$

Multiply $- 4 (4 \cdot 4)$ .

Multiply $4$ by $4$ .

$64 - 4 \cdot 16$

Multiply $- 4$ by $16$ .

$64 - 64$

Subtract $64$ from $64$ .

$0$